## Plus Two Accountancy Chapter Wise Questions and Answers Chapter 2 Spread Sheet

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## Kerala Plus Two Accountancy Chapter Wise Questions and Answers Chapter 2 Spread Sheet

Question 1.
The best way to get started in Libre Office calc is _____
Application → Office → LibreOffice Calc

Question 2.
___________ is a configuration of rows and columns

Question 3.
A spread sheet is also known as ____________
(a) Work book
(b) Work area
(c) Work sheet
(c) Work sheet

Question 4.
____________ in spread sheet are horizontal vectors while ______ are vertical vectors
Rows, columns

Question 5.
(a) Record data
(b) Calculate data
(c) Compare data
(d) All the above
(d) All of the above

Question 6.
Each cell value can either be an independent (basic) value or it may be derived on the basis of ____________.
Arithmetic expression or a function.

Question 7.
A file in LibreOffice Calc is known as a ______
(a) Work sheet
(b) Page
(c) Work book
(d) All the above
(c) Work book

Question 8.
A work book is a collection of a number of ______
Work Sheets

Question 9.
Where is the address of the active cell displayed?
(b) Status Bar
(c) Name Box
(d) Formula Bar
(c) Name Box

Question 10.
Which command reverses the last action performed in the worksheet?
(a) Cut
(b) Undo
(c) Redo
(d) Paste
(b) Undo

Question 11.
__________ is a text or special character or descriptive information for rows or columns.
Label

Question 12.
A formula must starts with a ___________ sign
(a) =
(b) >
(c) *
(d) {}
(a) =

Question 13.
_______ Function is commonly used to get the addition of various numbers orthe contents of various cells.
Autosum (Σ)

Question 14.
The cell A5 indicate Column _______ and Row _____
Column A & Row 5

Question 15.
The dark box which distinguishes the active cell is called _______
Cell Pointer

Question 16.
One or more cells selected is called ______
a range

Question 17.
Without the equal sign, the entry in a cell is treated as _________
(a) Text
(b) Label
(c) TextorLabel
(d) None of the above
(c) Text or Label

Question 18.
Libre Office calc has three type of cell entries, they are _______ , ______and _______
Value, Label and Formula.

Question 19.
Which command allows you to reverse an undo command?
(a) Redo
(b) Repeat
(c) Reset
(d) Reverse
(a) Redo

Question 20.
Which cell alignment is assigned to most values by default?
(a) Right
(b) Left
(c) Centre
(d) None of the above
(b) Left

Question 21.
Which function automatically totals a column or row of Values?
(a) TOTAL
(c) SUM
(d) AVG
(c) SUM

Question 22.
Which Mathematical Operator is represented by an asterisk (*)
(a) Exponentiation (square)
(c) Subtraction
(d) Multiplication
(d) Multiplication

Question 23.
How many blank work sheets are shown when a new workbook is created?
(a) One
(b) Two
(c) Three
(d) Four
(c) Three

Question 24.
The cell co-ordinate in the formula are known as ………….
cell references

Question 25.
IF function is …………….
Logical function

Question 26.
The cell references for cell range of G2to M12 is …………….
(a) G2.M12
(b) G2: M12
(c) G2; M12
(d) G2 – M12
(c) G2: M12

Question 27.
If 4/6 entered in a cell without applying any format, LibreOffice Calc will treat this as
(a) Fraction
(b) Number
(c) Text
(d) Date
(d) Date

Question 28.
The cell labelled F5 refers to …………….
(a) Row F column 5
(b) Column F row 5
(c) Function available in cells
(d) Function key F5
(b) Column F row 5

Question 29.
LibreOffice Calc is a FOSS. What is FOSS?
Free and Open Source Software.

Question 30.
Which among the following is not a spreadsheet software.
(a) MS Office Excel
(b) Open Office Spredsheet
(c) Libre Office Calc
(d) MS Office Word
(d) M S Office Word

Question 31.
How many worksheets can be made as active worksheet at a time?
(a) 1
(b) 2
(c) 3
(d) 4
(a) 1

Question 32.
The name of the worksheet will be shown in the ______ at the bottom left of the windows.
Sheet Tab

Question 33.
To add column in a worksheet, click __________, there we get an option to add column.

Question 34.
A ………… is identified by a combination of a column header (letter) and a row header (number)
cell

Question 35.
_______ is a group of adjacent cells that forms a rectangular area.
Range

Question 36.
Which among the following is used as the range operator
(a) ;
(b) :
(c) /
(d) #
(b) :

Question 37.
One ENTER key stroke means
(a) One cell down
(b) One cell up
(c) One cell right
(d) One cell left
(a) One cell down

Question 38.
………………. Function counts the number of cells which contain any value.
(COUNT, COUNTA, COUNT BLANK, COUNTIF)
COUNTA

Question 1.
Match the following

 A B 1. Rows 1. Intersection of a row & a column 2. Columns 2. Numerical numbers from top to bottom 3. Cell 3. Unique identification code of a cell 4. Cell address 4. Alpha characters from left to right

 A B 1. Rows 1. Numerical numbers from top to bottom 2. Columns 2. Alpha characters from left to right 3. Cell 3. Intersection of a row & a column 4. Cell address 4. Unique identification code of a cell

Question 2.
What do you mean by spreadsheet?
Spreadsheet application is a computer program that allows to record, calculate and compare numerical or financial data. Using a spreadsheet program. We can store a lot of data in the worksheet and also arrange and analyse the data by using different functions and formulae for the meaningful object.

It is used to establish relationship between two or more sets of data. Libre Office Calc, MS Office Excel, Open Office Spreadsheet etc. are examples of spreadsheet software.

Question 3.
Give a short note on

1. Work book
2. Work sheet

1. Workbook:
A file in spread sheet is known as a workbook. A work book is a collection of a number of work sheets.

2. Work sheets:
The work area which consists of rows and columns in a spreadsheet is called a worksheet. By default three work sheets-sheet 1, sheet -2, sheet -3 are available in work book.

Question 4.
Explain about rows and columns in Libre Office Calc?
1. Rows:
Rows are the horizontal vectors in the worksheet. These are numbered numerically from Top to Bottom.

2. Columns:
Columns are vertical vectors in the worksheet. These are referred by alpha characters from left to right such as A, B, C, …, AA, AB, AC …etc.

Question 5.
What do you mean be Relative cell Reference?
1. Relative Cell references:
By default cell reference is relative; which means that as a formula or function is copied and pasted to other cells, the cell references in the formula or function change to reflect the new location.

Question 6.
Define the following

1. Label
2. Formula

1. Labels:
Descriptive information for rows or columns in the form of a text or a special character is called Label.

2. Formula:
The formula means a mathematical calculation on a set of cells. The formula must start with an = (equal to) sign. When a cell contains a formula, it often contains reference to other cells. Eg:= Basic pay + DA + HRA

Question 7.
List down any two features fo Spreadsheet.

• A spreadsheet is a configuration of rows and columns.
• A spreadsheet is also known as worksheet.

Question 8.
Name the different spreadsheet software available.
LibreOffice Calc, MS Office Excel, Open Office Spreadsheet.

Question 9.
Briefly explain any two Date and Time functions availabe in LibreOffice Calc
1. TODAY():
It is the function for today’s date in the worksheet. This helps to update the date value when we reopen the spreadsheet or modify the values of the document
Syntax: =TODAY()

2. NOW ():
It is the function for today’s date and present time. This helps to update the date and the time value when the cell value is modified.
Syntax: =NOW()

Question 10.
Give the Syntax for

1. YEAR()
2. DATE()

1. YEAR()
Syntax: = YEAR (Date value) OR = YEAR (“Date”)

2. DATE()
Syntax: = DATE (Year, Month, Day)

Question 11.
Complete the table by using ROUNDUP()

1. 1880
2. 1900

Question 12.
What are the Text Manipulation Function in LibreOffice Calc

• TEXT
• CONCATENATE

Question 13.
Give the explanation of the following errors
Error Message

1. # DIV/o!
2. VALUE!

1. # DIV/0! → When a number is divided by zero
2. VALUE! → When a wrong argument is given in a fromula

Question 14.
Spot the correct pairs by observing the nature of software, and give justification
(a) Microsoft Excel and LibreOffice Calc
(b) Linux and Tata Ex.
(c) Windows and MS Office
(d) GINUGhata and Microsoft Access
(a) Microsoft Excel and LibreOffice Calc. Both are spread sheet packages.

Question 1.
What are the advantage of Libre Office Calc?

1. It is both free software and open source software.
2. It can be used to calculate, analyse and manage data.
3. Libre Office Calc is available for a variety of platforms including Linux, OSX, Microsoft windows and Free BSD.

Question 2.
Give the cell address or range reference in the following situations.

1. Cell at 10th column and 6th row.
2. Cell at 27th column and 15th row.
3. Range starting from 5th column, 9throw and spread till 12th column and 15th row.

1. Cell at 10th column and 6th row = J6.
2. Cell at 27th column and 15th row = AA15.
3. Range starting from 5th column, 9th row and spread till 12th column and 15th row = E9: L15.

Question 3.

1. What is FOSS?
2. What are the benefits of using FOSS?

1. FOSS means Free and Open Source Software
2. The benefits of using FOSS:
• Decreased software costs.
• Increased Security and stability.
• Any one can use, copy, study and change the software in any manner.
• Source code is openly shared.

Question 4.
How can we save Libre Office Calc file?
Step 1: Go to the File menu

Step 2: Click on Save
Save

OR

Step 1: & Step 2 – Press Ctrl + S
Ctrl + S

Step 3: Type the file in the name field instead of default name Untitled 1
Name field

Step 4: Choose the place where we want to save the new file.

Step 5: Click on Save

Question 5.
Write the steps to be followed to

1. Rename a worksheet
2. Delete a worksheet
3. Copy a worksheet

1. Rename a worksheet:
Step – 1 Select the work sheet in the Sheet Tab which we want to Rename.

Step – 2 Right click and select Rename sheet from the drop up menu

Step – 3 Type new name in the Name field and press OK button

2. Delete a worksheet:
Step – 1 Select the worksheet in the Sheet Tab which we want to delete

Step – 2 Right click and select Delete sheet from the drop up menu

Step – 3 Click on Yes to the conformation question.

3. Copy a worksheet:
Step – 1 Click on blank rectangle Top left corner of the worksheet (Range Adress A1: AM J1048576)

Step – 2 Move the curser inside the worksheet and Right click the mouse.

Step – 3 Click on Copy from the dropdown menu.

Step – 4 Open the worksheet where we want to copy the sheet

Step – 5 Right click on cell A1. Click on Paste.

Question 6.
Give the cell address or range reference in the following situations.

1. Cell of 10th column and 9th row
2. Range starting from 2nd column 4th row and spread till 8th column 12th row
3. Range starting from 4th column 5th row and spread till 10thcolumn 15th row

1. J9
2. B4: H12
3. D5: J15

Question 7.
What is the purpose of the COUNTIF function?
COUNTIF():
This function counts the number of cells within a given that meet the criteria or condition.
Syntax: = COUNTIF (Range, Criteria)

Question 8.
Write the command to calculate the State Life Insurance Premium (SLI) of an employee using IF Function. The condition is SLI Premium Rs. 500/-below Basic Pay (BP) of Rs. 15000/- and for others Rs. 800/- (BP is given in cell C3)
= IF(C3 < 15000, 500, 800)

Question 9.
4 numbers are entered in Libre Office Calc spreadsheet starting from cell A1 to A4. Write any two formulae for getting total of those numbers in the cell A5

1. A5 = A1 + A2 + A3 + A4
2. A5 = Σ(A1 : A4)

Question 10.
For preparation of Payslip of an employee, Govind entered Basic Pay in cell B2 of a worksheet in LibreOffice calc. The D.A. is 76% of Basic Pay and Gross Salary is the sum of Basic Pay and DA. In order to calculate the amount of DA in cell C2 and Gross salary in cell D2, what entries are to be made?
Basic Pay → B2
DA → C2
Gross salary → D2
C2 = B2 * 76%
D2 = B2 + C2

Question 11.
Consider the following features of a software tool. Identify the software.

1. It can be used as a text editor
2. List out the important uses of this software

1. LibreOffice calc has the above mentioned features.
2. Importance of LibreOffice calc.
• It can be used for the preparation of statement of depreciation.
• It can be used for preparation of Payroll of employees.
• It can be used for the preparation of the loan re-payment schedule.

Question 12.
Complete the following.

1. One cell down → arrow key
2. One cell up → …………………………
3. One cell left → …………………………
4. One cell right → ………………………

2. Up arrow key
3. Left arrow key
4. Right arrow key

Question 13.
Can you give some key navigations and short cut in LibreOffice calc?
We can move around a worksheet through four arrow keys

1. Left-arrow key
2. Right arrow key
3. Up arrow key
4. Down arrow key

The mouse can also be used for navigation in a spreadsheet except for data entry. Some common operations/navigations are listed below:

 Movement Keystroke (Press Key) One cell up Up arrow key/ Shift + Enter key One cell down Down arrow key/ Enter key One cell right Right arrow key/ Tab key One cell left Left arrow key / Shift + Tab key Top of sheet (Cell A1) Ctrl + Home Key Move to last cell containing data Ctrl + End Key Move to beginning of the Row Home Key or Ctrl + Left arrow key Move to last filled cell in column End key

Question 14.
What commands are used to insert a column and delete a column in LibreOffice Calc?
1. To insert a column:
To insert a column click a cell in the column immediately to the right of where you want to insert the new column. Then on the Insert menu, click Columns.

2. To delete a column:
Select the column you want to delete. On the Edit menu, click Delete.

Question 15.
Give the procedure to insert a new worksheet and to delete a worksheet.
To insert a new worksheet, right click the worksheet, select ‘insert’. To delete a worksheet, select the sheet you want to delete and ‘click delete sheet’ on the edit menu.

Question 16.
Give the cell address or range reference in the following situations.

1. Cell at 12th Column and 8th row.
2. Range starting from 6th Column 10th row and spread till 12th Column and 16th row.

1. L8.
2. F10: L16

Question 17.
Name the appropriate Statistical functions.

1. Number of cells contain numbers.
2. Number of cells contain any value.
3. Number of empty cell.
4. Number of cells that meet the given criteria.

1. COUNT
2. COUNTA
3. COUNTBLANK
4. COUNTIF

Question 18.
What is the use of financial function ACCRINT in LibreOffice Calc
ACCRINT ():
This function returns the accrued interest for a security that pays periodic interest.
Syntax: = ACCRINT(Issue, First_Interest, settlement, rate, Par, frequency, basis, calc_method)

Question 19.
Explain the difference between relative cell reference and absolute cell reference?
1. Relative Cell references:
By default cell reference is relative; which means that as a formula or function is copied and pasted to other cells, the cell references in the formula or function change to reflect the new location.

2. Absolute Cell reference:
The absolute cell reference consists of the column letter and row number surrounded by dollar ($) signs. Eg$A$5. An absolute cell reference is used when we want a cell reference to stay fixed on a specific cell. Question 20. What is the use of PIVOT TABLE? Answer: Preparation of reports using Pivot Tables: A Pivot Table is a way to present information in a report format. A Pivot Table report provides enhanced layout, attractive and formatted report with improved readability. There are two types of data table. 1. One-Variable Data Table (One – Variable ) 2. Two-Variable Data Table (Two-Variable) • The one variable Data Table allows us to identify a single decision variable in our model and see how changing the values for that variable affects the values calculated by one or more formulas in our model. • The two variable Data table allows us to specify two decision variables and a variety of inputs and only a single formula. ### Plus Two Accountancy Spread Sheet Five Mark Questions and Answers Question 1. Define the following 1. Cell 2. Range 3. Worksheet 4. Workbook Answer: 1. Cell: The intersection of a row and a column is called a cell. A cell is identified by a combination of an alpha – numeric character eg: A1, B6, C10, etc. This alpha numeric character is called cell address. Hence each cell has a unique address. 2. Ranges: Range is a group of adjacent cells that forms a rectangular area. A range is specified by giving the address for first cell in range and the last cell in the rage, eg: range starting from A10 to A20 is written as A10: A20 where colon (:) is the range operator. 3. Work sheets: The work area which consists of rows and columns in a spreadsheet is called worksheet. By default three worksheets-sheet 1, sheet -2, sheet -3 are available in work book. 4. Workbook: A file in spread sheet is known as a workbook. A work book is a collection of a number of work sheets. Question 2. What are the different spreadsheet reference functions in Libre Office Calc? Answer: Spreadsheet Reference Functions: The important spreadsheet reference functions are 1. LOOKUP () functions: The LOOKUP function returns a value either from a one-row or one-column range or from an array. The lookup function has two syntax forms: Vector form and Array form. The vector form of LOOUP looks in a one-row or one column range (known as a vector) for a value, and then returns a value from the same position in a second one-row or one-column range. The array form of LOOKUP looks in the first row or column of an array for the specified value, and then returns a value from the same position in the last row or column of the array. LOOKUP (Vector from) Syntax: = LOOKUP (search criterion, Search vector, Result vector) LOOKUP (Array form) Syntax: =(LOOKUP (lookup_value, array) 2. VLOOK UP (): VLOOK UP is the vertical LOOKUP function. Use VLOOK UP to search the first column (columns are vertical) of a block of data and return the value from another column in the same row. Syntax: = VLOOKUP (Search criterion; Array; Index; Sort Order) 3. HLOOKUP ( ): It is the Horizontal LOOKUP function, searches for a value in the first row of a table array and returns the corresponding value in the same column from another row of the same table array. Syntax: HLOOKUP (search criteria; index; sorted) Question 3. Give the cell address or range reference in the following situations. 1. Cell at 10th Column and 9th row. 2. Range starting from 2nd Column 4th row and spread till 8th Column and 12th row. Answer: 1. J9. 2. B4: H12 Question 4. What are the logical functions in LibreOffice Calc Answer: Logical Functions: Logical functions are used for comparison and checking a test condition. The major logical functions are IF, AND and OR. Question 5. Explain the steps involved to insert a new work sheet in LibreOffice Calc Answer: Steps involved to insert a new work sheet in LibreOffice Calc. Step 1 – Click on the [+] button in the sheet Tab OR Step 1 – Click on the work sheet in the sheet Tab Sheet Tab Step 2 – Right click the mouse Step – 3 Select insert sheet from the Drop up menu box Drop up Step 4- Add number of sheets and give name, press OK Question 6. You are required to prepare a rank list for admission to the B.Com course. The Index mark is calculated as follows. Sum of mark secured in Plus 2, Mark obtained in Accountancy and -25% of Mark obtained in Business studies. Give the entries in Libre Office Calc to get the index mark. Answer: • A1 → Total Mark • B1 → Mark in Accountancy • C1 → Mark in Business Studies • D1 → Index Mark • A2 → Enter the Marks • B2 → Enter the Marks • C2 → Enter the Marks • D2 → =A2 + B2 + (C2 * 25%) Question 7. Match the following:  A B 1. One cell to the left 1. Right arrow key 2. To cell A1 2. Ctrl + End 3. One cell to the right 3. Ctrl + Home 4. To the last cell in the worksheet that contains data 4. Shift + Tab Answer:  A B 1. One cell to the left 1. Shift + Tab 2. To cell A1 2. Ctrl + Home 3. One cell to the right 3. Right arrow key 4. To the last cell in the work sheet that contains data 4. Ctrl + End Question 8. The monthly sales of a company for the first six months are given below:  A B 1. January 25000 2. February 15000 3. March 28000 4. April 32000 5. May 20000 6. June 30000 1. Find the total sales for the six months 2. Find the average sales of the six months 3. Find the lowest sales of the six months 4. Find the highest sales of the six months Answer:  A B 7. Total sales = SUM (B1:B6) 8. Average sales = Average (B1:B6) 9. Lowest sales = MIN (B1:B6) 10. Highest sales = MAX(B1:B6) Question 9. Give the range reference in the following cases. 1. Range beginning from 1st column, 1st row and ending 16th column, 8th row 2. Range beginning from 5th column, 7th Row and ending 27th column, 37th row Answer: 1. A1: P8 2. E7: AA37 Question 10. Match the following:  A B a) Today a) Today’s date & Time b) Now b) Convert date into corresponding value c) Day c) Today’s date d) Date value d) Day of the data referred in the formula Answer:  A B a) Today a) Today’s date b) Now b) Today’s date & time c) Day c) Day of the date referred in the formula d) Date value d) Convert date into corresponding value Question 11. Give the cell address or range reference in the following situations 1. Cell at 8th column and 10th row 2. Cell at 27th column and 6th row 3. Range starting from 5th column, 9th row and spread till 12th column and 15th row Answer: 1. H10 2. AA6 3. E9: L15 Question 12. What are the steps to be followed for naming cells and ranges. Answer: Step 1 – Select the cells or ranges that are to be named. Step 2 – Select Define Range from the Data menu Data. Step 3 – This will display a dialogue box us “Define Database Range”. It will provide a place to enter “Name”. Step 4 – Click OK on the dialogue box. ### Plus Two Accountancy Spread Sheet Practical Lab Work Questions and Answers Question 1. The following marks are obtained by 8 students in an examination. Ascertain the grade obtained by students based on the following criteria Procedure: Step 1 – Open Libre Office Cal work sheet Applications → Office → Libre Office calc Step 2 – Enter the data in the given cells Step 3 – Enter the following formula in cell D2 = IF(C2 < 30, “FAIL”, IF(C2 < 40, “D+”, IF(C2 < 50, “C”, IF(C2<60, “C+”, IF(C2 < 70, “B”, IF (C2 < 80, “B+”, IF(C2 < 90, “A”, IF(C2 < 100, “A+”)))))))) Step 4 – Drag the formula to D9 Output: Question 2. The sales made by 6 salesmen during three months are given below. You are required to prepare a statement showing the total sales of each salesman and total sales of the firm. Procedure: Step 1 – Open LibreOffice calc worksheet Applications → Office → LibreOffice Calc Step 2 – Enter the following data in the given cells Step 3 – Enter the given formula in cell E2 = B2 + C2 + D2 Step 4 – Drag the formula to E7 to get the total sales of each salesman Step 5 – Enter the given formula in cell E8 to get the total sales of the firm = SUM (E2: E7) Output: Question 3. The monthly production of a company are given below  Month Production (Units) January 25000 February 20000 March 22000 April 18000 May 19000 June 24000 1. Find the total production for the six months 2. Find the average production of the six months 3. Find the number of months during the period 4. Find the lowest production of the six months 5. Find the highest production of the six months Procedure: Step 1 – Open LibreOffice Calc worksheet Applications → Office → LibreOffice Calc Step 2 – Enter the following data in the given cells Step 3 – Enter the following formula in the given cells  B8 = SUM (B2:B7) B9 = AVERAGE(B2: B7) B10 = COUNT (B2:B7) B11 = MIN (B2:B7) B 12 = MAX (B2:B7) Output: Question 4. For the recruitment of managers in different departments of a company, Applicant’s age should be greater than 35 and less than 45 as on 31/03/2018. Write the Spreadsheet statement to test when a candidate is eligible for recruitment or not, when his/ her date of birth is entered in a cell as input Procedure: Step 1 – Open LibreOffice Calc Spread sheet. Applications → Office → LibreOffice Calc Step 2 – Enter the given data in the following cells Step 3 – Enter the date of birth in cell B2 Step 4 – Enter the following formula in cell B3 = Round ((B1-B2)/365,0). Then the age will display in the cell B3. Step 5 – Enter the following formula in cell B4 to test the eligibility of the candidate = IF(B3<35, “Not eligible”, IF(B3>45, “Not eligible”, “Eligible”) OR = IF (AND (B>34, B3<46), “Eligible”, “Not eligible”) Note: The data value entered in cell B2 and B3 are to be formatted as “Date” Question 5. The given table shows name of employees, Designation and monthly salary paid for different employees in Jose Traders. Find out the following: 1. The total monthly salary by naming range (TOTAL SALARY) 2. The total monthly salary paid to marketing managers (MM) in the firm 3. The name of employees with a monthly salary of Rs.30000 by using LOOK UP function. Procedure: Step 1 – Open LibreOffice Calc worksheet Applications → Office → LibreOffice Calc Step 2 – Enter the data in the appropriate cells Step 3 – Naming a range Select the range which shows monthly salary ie C2: C7 click on “Data” from the menu bar. Select “Define Range” Type the name “TOTAL_SALARY” in the name box and press OK or Enter key Select the Range (C2: C7) → Data → Define Ranges Type TOTAL_SALARY. Press OK/Enter Key Step 4 – Enter the following formulas in respective cells .  B8 = SUM (TOTAL_SALARY) B9 = SUMIF(B2:B7, “MM”, C2:C7) B10 = LOOKUP(30000, C2:C7, A2:A7) Output: Question 6. The following Data is given in the form of a Table. • How many cells contain numbers only? • How many cells contain any value? • Count the number of cells containing the value exceeding 500. • How many blank cells are there in the table? Procedure: Step 1 – Open LibreOffice Calc Applications → Office → LibreOffice Calc Step 2- Enter the given details in appropriate cells. Step 3 – Enter the given details and formula in the Following cells. Step 3 – Enter the given details and formula in the Output: Question 7. The following details are given Find out • Find the name of student whose admission number is 8267 • Look up value 8136 and locate the fee paid status by using VLOOKUP • Look up the name of student against admission number 8124 • Ad. No. of student who paid fee Rs. 580 Procedure: Step 1 – Open LibreOffice Calc worksheet Application → Office → LibreOffice Calc. Step 2 – Enter the details in the given cells Step 3 – Enter the given details and formula in the following cells  A 8 Name of student Ad.No.8267 9 Fee paid status of Ad No.8136 10 Name of student Ad. No.8124 11 Ad.No. of student, paid Rs.580  B 8 = LOOKUP(8267,A2:A7,B2:B7) 9 = VLOOKUP(8136,A2:C7,3,0) 10 = LOOKUP(8124,A2:A7,B2:B7) 11 = VLOOKUP (8370,A2:C7,3,0) Output: Question 8. The marks in Accountancy of some students are given below.  Name Mark Priya 89 Indira -ab- Sindhu 56 Reny 64 Beena 49 Bindhu 50 Resmi -ab- Calculate: 1. Number of students in the class 2. Number of students appeared in the Accountancy examination 3. Total marks in Accountancy examination 4. Average Marks in Accountancy examination 5. Lowest mark in Accountancy 6. Highest mark in Accountancy Procedure: Step 1 – Open LibreOffice Calc Work sheet Application → Office → LibreOffice Calc. Step 2 – Enter the given data in appropriate cells. Step 3 – Enter the following details and formula in the given cells Output: Question 9. Mark summary of some students are given below. Calculate 1. Number of cells containing 90 marks 2. Count the number of paper scored less than 40 3. Find the result of each student. (Pass or Fail) minimum mark required to pass is 30 Procedure: Step 1 – Open LibreOffice Calc worksheet Application → Office → LibreOffice calc Step 2 – Enter the given data in appropriate cells Step3 – Enter the following details and formula in appropriate cells  A8 Number of cells containing 90 mark B8 = COUNTIF(B2: G7, “90”) A9 Count the number of paper scored less than 40 Mark B9 = COUNTIF(B2: G7, “40”) Step4 – Find the result of the student 1ststep – Count the number of marks less than 30 scored by each student For this, Enter the formula in H2 =COUNT IF (B2: G2, “<30”) Drag the equation to H7 2nd step – Based on the result in H2: H7 range, we can find out the result in I2 cell by giving the following formula =IF(H2 = 0, “PASS”, “FAIL”) Drag (Copy) the formula to I7 Output: Question 10. List of debtors and creditors, and the amount due from them are given below Calculate the total amount of receivables and payables using SUMIF functions. Procedure: Step -1 Open Libre Office Calc worksheet Applications → Office → LibreOffice calc Step 2 – Enter the details in the given cells. Output: Question 11. Calculate Income Tax of following employees based on the following criteria. Conditions 1. Tax rate is 40% of Total taxable Income. 2. For male, standard deduction is 150,000 3 For female, if taxable income is less than or equal to Rs.4,00,000, then the standard deduction is 2,00,000, otherwise 1,50,000 Procedure: Step 1 – Open LibreOffice Calc worksheet Application → Office → LibreOffice calc Step 2 – Enter the given details in the given range Step 3 – Calculation of Tax Enter the formula in D2 cell and drag with the fill handle up to D8 = IF(B2 = “Male”, (C2 – 150000)*40%, IF (AND(C2 = “Female”, C2 <= 400000), (C2 – 200000)*40%, (C2 – 150000)*40%)) Output:  Name of Employee Tax Manoj 60,000 Praveena 1,20,000 Naveen 2,20,000 Riya 2,08,000 Rohit 1,40,000 Latha 80,000 Arya 2,84,000 Question 12. For SI selection in Kerala polices there is a physical test, which consists of three items. A candidate has to qualify ANY ONE of the three tests to qualify for the final. The standard for the physical test is given below. • Shot put: 5 meters or above. • Ball throws 50 meters. • 500-meter race within 5 minutes. The following data is furnished: Check whether the candidates quality or not. Procedure: Step 1 – Open LibreOffice Calc worksheet Application → Office → LibreOffice calc Step 2 – Enter the details in the form of a Table Step 3 – Enter the following formula in F2 and drag with fill up to F6 = IF(OR(C2>=5, D2>=50, E2<=5), ‘‘Qualified”, “Not Qualified”) Output:  Chest No. Result 203 Qualified 216 Qualified 275 Qualified 304 Not Qualified 361 Qualified Question 13. Calculate DAY, MONTH and YEAR of 36525 Procedure: Step 1 – Open LibreOffice Calc worksheet. Step 2 – Enter the details in appropriate cells. Output: Question 14. Calculate the Date value of 28/10/1978/ Procedure: Step 1 – Open LibreOffice calc work sheet Application → Office → LibreOffice Calc Step-2 – Enter the given details in Cell A1 = DATEVALUE (“28/10/1978”) Output: Question 15. Find the age of Resi Jos based on her date of birth and today’s date Date of birth 06-05-1981. Procedure: Step 1 – Open Libre office Calc work sheet Application officer LibreOffice calc Step 2 – Enter the following details in appropriate cells. Output: Question 16. Below is given the table showing the name, department, and salary paid for different employees • Find number of employees in the firm. • Find number of employees in Production Department. • Find the total monthly salary paid in Purchase Department. • Find the total monthly salary paid in Finance Department. Procedure: Step 1 – Open a new blank work sheet in LibreOffice Calc. Step 2 – Enter the following details as given below. Step 3 – Enter the following text in different cells as given below.  Cell Text A9 No. of employees in the firm A10 No. of employees in the production department A11 Total monthly salary paid in purchase depart­ment A12 Total monthly salary paid in finance depart­ment Step 4 – Enter the following formula in different cells as given below.  Cell Formula B9 = COUNTA(A2: A8) B10 = COUNTIF(B2: B8, “Production”) B11 = SUMIF (B2: B8, “Purchase”, C2: C8) B12 = SUMIF (B2: B8, “Finance”, C2: C8) Output: Question 17. Below is given the table showing the Name, Department, and Salary paid for different employees. • Name the employee name column as “Emp Name”, Department column as “Dept” and monthly salary column as “Salary”. • Find the total monthly salary. procedure: Step 1 – Open a blank worksheet in LibreOffice Calc. Step 2 – Enter the following details in respective cells. Step 3 – Select the range A2: A6, From the Data tool menu, select “Define Range” and – give name as “ Emp Name” and click (OK) button. Step 4 – Select the range B2: B6, From the Data tool menu, select “Define Range” and give name as “Dept” and click (OK) button. Step 5 – Select the range C2: C6, From the Data tool menu, select “Define Range” and give name as “Salary” and click (OK) button. Step 6 – Enter the following formula to find out the total monthly salary.  Cell Text / Formula A 7 Total Monthly Salary B 7 = SUM (Salary) Output:  Total Monthly Salary 12500 Question 18. Below is given the table showing the Name, Class, and Fees due to different students. • Find out the total fees due from the students. • Find the average amount of fees • Find the highest amount of fees • Find the lowest amount of fees Procedure: Step 1 – Open a new blank worksheet in LibreOffice Calc Step 2 – Enter the following details in the worksheet as follows. Step 3 – Enter the following text in respective cells.  Cell Text A9 Total Fees due A10 Average Fees A11 Highest amount of fees A12 Lowest amount of fees Step 4 – Enter the following formula in respective cells  Cell Formula B9 = SUM (D2: D8) B10 = Average (D2: D8) B11 = Max (D2;D8) B12 = Min (D2: D8) Output:  Total Fees Due 2700 Average Fees 386 Highest Amount of Fees 625 Lowest Amount of Fees 60 Question 19. From the given values, calculate the following: • Find the number of values • Find the total sum of the values • Find the average • Find the largest value • Find the smallest value Procedure: Step 1 – Open a new blank worksheet in LibreOffice Calc Step 2 – Enter the values in the work sheet as follows. Step 3 – Enter the following text in the respective cells.  Cell Text A8 Number of values A9 Sum of the values A10 Average AH Largest value A12 Smallest value Step 4 – Enter the following formula in the respective cells.  Cell Formula B8 = COUNT (A1: A7) B9 = SUM(A1: A7) B10 = AVERAGE/A1: A7) B11 = MAX/A1: A7) B12 = MIN(A1: A7) Output:  Number of values 7 Sum of the values 3000 Average 429 Largest value 700 Smallest value 200 Question 20. Prepare a statement showing advance tax collected form the employees @ 10% of the yearly salary from those who receive Rs. 500000 or more.  Employees Yearly salary Fijo 855000 Joshy 650000 Roby 720000 Bose 425000 Prince 570000 Binoy 380000 Procedure: Step 1 – Open a new blank worksheet in LiberOffice Calc. Step 2 – Enter the following details in respective cells. Step 3 – Select the range A2: A7, From Data Tools menu, select ‘Name a Range’ and give name as “Employees” and click (OK) button. Step 4 – Enter the text /formula in the following cells.  C 1 Advance Tax 2 = IF (B2>=500000, B2*10%, 0) 3 4 5 6 7 Step 5 – Copy formula to C3: C7 to the last employee. Step 6 – Enter “Total Advance Tax” in cell B8 and enter the formula ‘‘SUM C2: C7” to get total amount. Output:  Fijo 85500 Joshy 65000 Roby 72000 Prince 57000 Question 21. Mrs. Leela, the class teacher is analysing the performance of her students in a class test. Find out • Total number of students • Number of students appeared in the class test • Number of students with no grade • Number of A+ holders • Number of B grade holders. Procedure: Step 1 – Open a new blank worksheet in LiberOfficeCalc Step 2 – Enter the following details in the respective cells. Step 3 – Enter the text /formula in the corresponding Output:  Total number of students 8 Students appeared in-class test 6 Students with no grade 2 Number of A+ holders 2 Number of B grade holders 1 Question 22. The monthly sales effected by 6 salesmen are given below. Calculate the commission earned by each salesman on the basis of the following rules.  Total sales Commission Less than 8000 Nil 8000- 10000 5% 10000- 12000 8% More than 12000 10% Procedure: Step 1 – Open a new blank worksheet in LibreOffice Calc. Step 2 – Enter the following details in the respective cells. Step 3 – Enter the formula = SUM (B2: D2) in cell E2 to get the total sales. Copy the formula to the last employee. Step 4 – Enter the formula = IF (E2 >= 12000, E2 * 10%, IF (E2 >= 10000, E2*8%, IF(E2 >= 8000, E2 * 5%,0))) Copy the formula to the last employee. Output: Question 23. ABC Ltd categorises their salesmen into four on the basis of sales targets achieved in each quarter. The criteria and sales are given below. Performance criteria Total sales – Grade More than 100000 – Excellent 50000-100000 – Good 30000-50000 – Average Less than 30000 – Bad Procedure: Step 1 – Open a new blank worksheet in LibreOffice Calc Step 2 – Enter the following details in the respective cells. Step 3 – Enter the formula in E2 to get total sales = SUM (B2: D2) Copy the formula to the last employee. Step 4 – Enter the formula in F2 to get the commission = IF(E2 >= 100000, “EXCELLENT”, IF (E2 >= 50000, “GOOD”, IF (E2 >= 30000, “AVERAGE”, “BAD”))) Copy the formula to the last employee. Output:  Ramesh BAD Suresh GOOD Mahesh AVERAGE Rajesh GOOD Sukesh GOOD Question 24. Below is given the name and address of some students. Combine and show details in an address format using CONCATENATE function. Procedure: Step 1 – Open a new blank worksheet in LiberOffice Calc Application → Office → LibreOffice Calc Step 2 – Enter the following details in appropriate cells Step 3 – Enter the following formula in F2 cell = CONCATENATE (A2, “ ”, B2, “ ”, C2, “ ”, D2, “ ”, E2) Step – 4 Copy down the formula up to the row of the last employee. Output:  Address Sanjan Kollannur Kechery 680579. Shaji Amala Bhavan Ollur 680514 Thrissur. Nithin MRA/258 Mannuthy 680007 Ernakulam. Question 25. Mr Venugoapl is planning to invest Rs. 10000 in the beginning of each year in an annual investment scheme. The interest rate is 8% and the term of the scheme is 10 years. Using FV function, find out how much amount he will get at the expiry of the scheme. Procedure: Step 1 – Open a new blank worksheet in LiberOffice Calc Step 2 – Enter the given detials and formula in diffemt cells Output:  Future value 156455 Question 26. Anakha Ltd. wants to select one machinery, out of the two alternatives available on the basis of net present value. The cost and inflows of these machineries are given below. Assuming annual interest rate of 10%, find out net present values of these two machineries. Procedure: Step 1 – Open a blank work sheet in LiberOffice Calc Step 2 – Enter the following details in respective cells. Step 3 – Enter the formula = NPV (10%, C2:F2) – B2 in G2 to get the net present value of semi automatic machinery. Copy the formula to G3 Output:  Machinery NPV Semi-Automatic 4683.42 Fully Automatic 52891.2 Question 27. Calculate Net Present Value (NPV) from the following data  Cost of Machinery 2000000 Cash inflows -1 year 60000 Cash inflows – II year 80000 Cash inflows – III year 82000 Cost of capital 12% Procedure: Step 1 – Open a new blank worksheet in LibreOffice Calc Step 2 – Enter the following details in the respective cells. Step 3 – Enter the formula in B6 = NPV (12%, B2:B4)-B1 to get NPV Output:  Net Present value 24287.1 Question 28. Write the Libre Office Calc formula to multiply a given number entered in a cell with the following conditions • If the cell value is less than 20, then multiply by 1 • If the cell value is greater than or equal to 20 but less than 40, then multiply by 2 • If the cell value is greater than or equal to 40 but less than 80, then multiply by 3 • If the cell value is greater than or equal to 80 but less than 100, then multiply by 4. • If the cell value is greater than or equal to 100, then display “Enter a value less than 100” Use nested IF function. Procedure: Step 1 – Open a blank work sheet in LibreOffice Calc Step 2 – Enter the following details in respective cells. Step 3 – Enter any value in cell A2; then the result will be in cell B2. Output:  Cell value Result 18 18 37 74 115 Enter value less than 100 85 340 Question 29. Salary detail of 8 employees are given below. Develop a formula to compute tax under the following conditions. 1. Tax rate-20% 2. For males, Rs. 2,00,000 is allowed as standard deduction. For females, if taxable income is less than or equal to Rs. 5,00,000, then Rs. 3,00,000 is allowed as standard deduction, otherwise Rs. 2, 50,000. Use suitable logical function. Procedure: Step 1 – Open a new blank worksheet in LibreOffice Calc Step 2 – Enter the following details in respective cells. Step 3 – Enter the formula in cell E2 and copy it to the last employee. =IF (C2 = “MALE”, (D2-20Q000)*20%, IF (AND(C2 = “FEMALE”, D2<=500000), (D2 – 300000) * 20%, (D2-250000)*20%)) Output:  Name Tax Elsy 40,000 Jose 90,000 Rosily 20,000 Rejina 40,000 Antony 1,00,000 Jessy 30,000 George 80,0000 Baby 60,000 Question 30. The recruitment process of language teachers in a school consists of three items like interview, group discussion and paper presentation. A candidate has to qualify any one of the three tests to qualify for the written test. The prescribed standard for the items are given below. • Interview – 16 score out of 20. • Group Discussion – 25 score out of 30. • Paper Presentation – 40 score out of 50 Other informations are also available. Write a formula using OR function to check whether a candidate qualify or not. Procedure: Step 1 – Open a blank work sheet in LiberOffice Calc. Step 2 – Enter the available data in work sheet Step 3 – Enter the formula in F2 and copy it to the last candidate = IF(OR (C2>=16, D2>=25, E2>=40) “Qualified for the written Test”, “Not Qualified”) Output: Question 31. Business studies, Accountancy and Economics are commerce subjects. Write a formula to check whether text is a commerce subject. If yes, print **** is a commerce subject, otherwise print **** is not a commerce subject. Write procedure based on the available hints Procedure: Step 1 – Open a blank work sheet in LiberOffice Calc Step 2 – Enter the text in the following cells. Step 3 – Enter the name of subject in A2 and type the formula in B2 and drag it = IF (OR (A2= “Business studies”, A2 = “Accountancy”, A2= “Economics”), A2 & “is a” & “Commerce Subject”, A2 & “is” & “not a commerce subject”) Output:  Subject Remarks Malayalam Malayalam is not a commerce subject Business studies Business studies is a commerce subject Chemistry Chemistry is not a commerce subject Mathematics Mathematics is not a commerce subject Accountancy Accountancy is a commerce subject. Question 32. ABC company issued a security with par value Rs. 50000 on 1/1/2013. The first interest date is 1-4-2013, the settlement date is 31-12-2015 an the annual coupon rate is 6%. The security’s payments are made quarterly, and a US (NASD) 30/360 day count basis is used. Use ACCRINT() function to calculated the accrued interest of a security that pays periodic interest. Procedure: Step 1 – Open a blank new worksheet in LibreOffice Calc. Step 2 – Enter the data in the following cells. Step 3 – Enter the formula in B9 = ACCRINT (B2, B3, B4, B5, B6, B7, B8) Output:  Accrued Interest 9000 Question 33. Prince took a loan of Rs. 500000 from banks @ 12% interest p.a. repayable after 15 years. Compute interest payable at the end of (a) First year (b) Second year (c) Fifth year and the last year. procedure: Step 1 – Open a new blank worksheet in LibreOffice Calc Step 2 – Enter the given details in respective cells Step 3 – Enter the given formula in respective cells. • B8 = CUMIPMT(B3/12, B2*12, B4, B5, B6, B7) • C8 = CUMIPMT(C3/12, C2*12, C4, C5, C6, C7) • D8 = CUMIPMT(D3/12, D2*12, D4, D5, D6, D7) • E8 = CUMIPMT(E3/12, E2*12, E4, E5, E6, E7) Output:  Year Interest First year 59316.92 Second year 57707.11 Fifth year 51545.84 Last year 4470.16 Question 34. Calculate the present value of an annuity that pays Rs. 3000 per month for a period of 5 years. The interest is 11.5% per annum and each payment is made at the end of the month. Assume the payments are made. • At the beginning of each month • At the end of each month Procedure: Step 1 – Open a new blank worksheet in LibreOffice Calc Step 2 – Enter the following data/ Formula in respective cells. Step 3 – Enter the formula as follows B6 = PV (B2/12, B3*12, B4, B5) C6 = PV(C2/12, C3*12, C4, C5) Output:  Present value – at the beginning 136409 Present value – at the end 136410 Question 35. The table given below shows the First name, Middle name and Last name of some employees. Show their Full name in the next column using CONCATENATE Function. Procedure: Step 1 – Open a new blank worksheet in Liber Office Calc Application → Office → Libre Office Calc Step 2 – Enter the following details in appropriate cells Step 3 – Enter the following formula in D2 cell = CONCATENATE (A2, “ ”, B2, “ ”, C2) Step 4 – Copy down the formula up to the row of last employee. Output:  FULL NAME Roby Antony Alappatt Hema Gangadharan Menon Cili Jose Vazhappilly Santhosh Jacob Kannanaikal ## Plus Two Maths Chapter Wise Questions and Answers Chapter 4 Determinants Students can Download Chapter 4 Determinants Questions and Answers, Plus Two Maths Chapter Wise Questions and Answers helps you to revise the complete Kerala State Syllabus and score more marks in your examinations. ## Kerala Plus Two Maths Chapter Wise Questions and Answers Chapter 4 Determinants ### Plus Two Maths Determinants Three Mark Questions and Answers Question 1. Using properties of determinants prove $$\left|\begin{array}{ccc}{x} & {y} & {x+y} \\{y} & {x+y} & {x} \\{x+y} & {x} & {y}\end{array}\right|$$ = -2(x3 + y3). Answer: = 2(x + y)(-x2 + xy – y2) = -2(x3 + y3). Question 2. If a, b, c are real numbers and $$\left|\begin{array}{lll}{b+c} & {c+a} & {a+b} \\{c+a} & {a+b} & {b+c} \\{a+b} & {b+c} & {c+a}\end{array}\right|$$ = 0, Show that a = b = c. Answer: 2(a + b + c) [(b – c) (c – b) – (b – a) (c – a)] =0 (a+b+c) = 0 (a + b + c) = 0 or (b – c) (c – b) = (b – a) (c – a) (a + b + c) = 0 or a = b = c. Question 3. Solve using properties of determinants. $$\left|\begin{array}{ccc}{2 x-1} & {x+7} & {x+4} \\{x} & {6} & {2} \\{x-1} & {x+1} & {3} \end{array}\right|$$ = 0 Answer: ⇒ (x – 1) (x2 + x – 6x + 6) = 0 ⇒ (x – 1)(x2 – 5x + 6) = 0 ⇒ (x – 1) (x – 3) (x – 2) = 0 ⇒ x = 1, x = 3, x = 2. Question 4. If $$\left|\begin{array}{cc}{3} & {x} \\{x} & {x}\end{array}\right|=\left|\begin{array}{cc}{-2} & {2} \\{4} & {1}\end{array}\right|$$, find the value of x. Answer: $$\left|\begin{array}{cc}{3} & {x} \\{x} & {x}\end{array}\right|=\left|\begin{array}{cc}{-2} & {2} \\{4} & {1}\end{array}\right|$$ ⇒ 3x – x2 = – 2 – 8 ⇒ x2 – 3x – 10 = 0 ⇒ x = 5, -2. Question 5. A = $$\left[\begin{array}{ccc}{1} & {-3} & {1} \\{2} & {0} & {4} \\{1} & {2} & {-2} \end{array}\right]$$ 1. Calculate |A| (1) 2. Find |adjA| {Hint: using the property A × adjA = |A|I} (1) 3. Find |3A| (1) Answer: 1. |A| = $$\left[\begin{array}{ccc}{1} & {-3} & {1} \\{2} & {0} & {4} \\{1} & {2} & {-2} \end{array}\right]$$ = – 28. 2. A × adjA = |A|I 3. |3A| = 27 × |A| = 27 × -28 = -756. Question 6. Using properties of determinants prove the following. Answer: = 2{-{-c){b{a – c)) – b(-c(c + a))} = 2{c(ab – cb) + b(c2 + ac)} = 2{abc – c2b + bc2 + abc)} = 4abc. ### Plus Two Maths Determinants Four Mark Questions and Answers Question 1. (i) If $$\left|\begin{array}{rrr}{1} & {-3} & {2} \\{4} & {-1} & {2} \\{3} & {5} & {2}\end{array}\right|$$ = 40, then $$\left|\begin{array}{ccc}{1} & {4} & {3} \\{-3} & {-1} & {5} \\{2} & {2} & {2}\end{array}\right|$$ = ? (a) 0 (b) – 40 (c) 40 (d) 2 (1) (ii) $$\left|\begin{array}{rrr}{3} & {-3} & {2} \\{12} & {-1} & {2} \\{9} & {5} & {2}\end{array}\right|$$ = ? (a) 120 (b) 40 (c) – 40 (d) 0 (1) (iii) Show that ∆ = $$\left|\begin{array}{ccc}{-a^{2}} & {a b} & {a c} \\{b a} & {-b^{2}} & {b c} \\{a c} & {b c} & {-c^{2}}\end{array}\right|$$ = 4a2b2c2 (2) Answer: (i) (c) 40 (ii) (a)120 (iii) ∆ = abc$$\left|\begin{array}{ccc}{-a} & {a} & {a} \\{b} & {-b} & {b} \\{c} & {c} & {-c}\end{array}\right|$$ take a, b, c from C1, C2, C3 Question 2. Answer: (i) $$\left|\begin{array}{ll}{2} & {4} \\{5} & {1}\end{array}\right|=\left|\begin{array}{ll}{2 x} & {4} \\{6} & {x}\end{array}\right|$$ ⇒ -18 = 2x2 – 24. ⇒ 2x2 = 6 ⇒ x2 = 3 ⇒ x = $$\pm \sqrt{3}$$. Question 3. Prove that $$\left|\begin{array}{ccc}{(b+c)^{2}} & {a^{2}} & {a^{2}} \\{b^{2}} & {(c+a)^{2}} & {b^{2}} \\{c^{2}} & {c^{2}} & {(a+b)^{2}}\end{array}\right|$$ = 2abc(a + b + c)3. Answer: = (a + b + c)2 × 2ab [(b + c) (c + a) – ab] = (a + b + c)2 × 2ab [bc + ab + c2 + ac – ab) = (a + b + c)2 × 2abc [a + b + c] = 2abc (a + b + c)3. Question 4. (i) Let the value of a determinant is ∆. Then the value of a determinant obtained by interchanging two rows is (a) ∆ (b) -∆ (c) 0 (d) 1 (1) (ii) Show that $$\left|\begin{array}{ccc}{a+b} & {b+c} & {c+a} \\{b+c} & {c+a} & {a+b} \\{c+a} & {a+b} & {b+c}\end{array}\right|=2\left|\begin{array}{lll}{a} & {b} & {c} \\{b} & {c} & {a} \\{c} & {a} & {b}\end{array}\right|$$ (3) Answer: (i) (b) -∆ (ii) Operating C1 → C1 + C2 + C3, we have Question 5. Test the consistency 3x – y – 2z = 2, 2y – z = -1, 3x – 5y = 3. Answer: The given system of equations can be put in the matrix form, AX = B, where |A| = 3(0 – 5) + 1(0 + 3) – 2(0 – 6) = 0 C11 = -5, C12 = -3, C21 = -6, C22 = 10, C23 = 6, C31 = 12, C32 = 5, C33 = 6 Therefore the system is inconsistent and has no solutions. Question 6. Consider the system of equations 2x – 3y = 7 and 3x + 4y = 5 1. Express the system in AX = B form. (1) 2. Find adj A (2) 3. Solve the system of equations. (1) Answer: 1. |A| = $$\left|\begin{array}{cc}{2} & {-3} \\{3} & {4}\end{array}\right|$$ = 8 + 9 = 17. 2. c11 = 4, c12 = -3, c21 = 3, c22 = 2, 3. The given equations can be expressed in the form AX = B, Question 7. (i) If A and B are matrices of order 3 such that|A| = -1; |B| = 3, then |3AB| is (a) -9 (b) -27 (c) -81 (d) 9 (1) (ii) If A = $$\left[\begin{array}{cc}{1} & {\tan x} \\{-\tan x} & {1}\end{array}\right]$$, Show that AT A-1 = $$\left[\begin{array}{cc}{\cos 2 x} & {-\sin 2 x} \\{\sin 2 x} & {\cos 2 x}\end{array}\right]$$ (3) Answer: (i) (c) -81 (since |3AB| = 27|A||B|). (ii) |A| = $$\left[\begin{array}{cc}{1} & {\tan x} \\{-\tan x} & {1}\end{array}\right]$$ = sec2x ≠ 0, therefore A is invertible. Question 8. Consider the determinant ∆ = $$\left|\begin{array}{ccc}{x} & {x^{2}} & {1+x^{3}} \\{y} & {y^{2}} & {1+y^{3}} \\{z} & {z^{2}} & {1+z^{3}}\end{array}\right|$$, Where x, y, z, are different. (i) Express the above determinant as sum of two determinants. (1) (ii) Show that if ∆ = 0, then 1 + xyz = 0. (3) Answer: (i) Given, ∆ = $$\left|\begin{array}{ccc}{x} & {x^{2}} & {1+x^{3}} \\{y} & {y^{2}} & {1+y^{3}} \\{z} & {z^{2}} & {1+z^{3}}\end{array}\right|=\left|\begin{array}{ccc}{x} & {x^{2}} & {1} \\{y} & {y^{2}} & {1} \\{z} & {z^{2}} & {1}\end{array}\right|+\left|\begin{array}{ccc}{x} & {x^{2}} & {x^{3}} \\{y} & {y^{2}} & {y^{3}} \\{z} & {z^{2}} & {z^{3}}\end{array}\right|$$ Given, ∆ = 0 ⇒ (1 + xyz)(y – x)(z – x)(z – y) = 0 ⇒ 1 + xyz = 0 ∵ x ≠ y ≠ z. Question 9. (i) The value of the determinant $$\left|\begin{array}{cc}{\sin 10} & {-\cos 10} \\{\sin 80} & {\cos 80}\end{array}\right|$$ is (a) – 1 (b) 1 (c) 0 (d) – 2 (1) (ii) Using properties of determinants, show that (3) $$\left|\begin{array}{lll}{a} & {a^{2}} & {b+c} \\{b} & {b^{2}} & {c+a} \\{c} & {c^{2}} & {a+b}\end{array}\right| = (b – c) (c – a) (a – b) (a + b + c)$$ Answer: (i) (b) Since, sin 10 cos 80 + cos 10 sin 80 = sin (10 + 80) =sin 90 = 1. (ii) Let C3 → C3 + C1 = (a + b + c)(b – a)(c – a)(c + a – b – a) = (a + b + c)(b – a)(c – a)(c – b) = (b – c)(c – a)(a – b)(a + b + c). Question 10. (i) Choose the correct answer from the bracket. Consider a square matrix of order 3. Let C11, C12, C13 are cofactors of the elements a11, a12, a13 respectively, then a11C11 + a12C12 + a13C13 is (1) (a) 0 (b) |A| (c) 1 (d) none of these. (ii) Verify A(adjA) = (adjA)A = |A|I for the matrix A = $$\left[\begin{array}{ll}{5} & {-2} \\{3} & {-2}\end{array}\right]$$ that, where I = $$\left[\begin{array}{ll}{1} & {0} \\{0} & {1}\end{array}\right]$$ (3) Answer: (i) (b) |A| (ii) |A| = $$\left|\begin{array}{cc}{5} & {-2} \\{3} & {-2}\end{array}\right|$$ = – 4 C11 = – 2, C12 = – 3, C21 = 2, C22 = 5 Hence A(adjA) = (adjA)A = |A|I. Question 11. Consider the following system of equations x + 2y = 4,2x + 5y = 9 1. If A = $$\left[\begin{array}{ll}{1} & {2} \\{2} & {5}\end{array}\right]$$, find |A| (1) 2. Express the above system of equations in the form AX = B (1) 3. Find adj A, A-1 (1) 4. Solve the system of equations. (1) Answer: 1. |A| = $$\left[\begin{array}{ll}{1} & {2} \\{2} & {5}\end{array}\right]$$ = 5 – 4 = 1 2. The given system of equation can be expressed in the form AX = B. 3. Cofactor matrix of A = $$\left[\begin{array}{cc}{5} & {-2} \\{-2} & {1}\end{array}\right]$$ 4. We have, x = 2, y = 1. Question 12. Consider the point X(-2, -3), B(3, 2), C(-1, -8) 1. Find the area of ∆ABC (2) 2. Find third vertex of any other triangle with same area and base AB. (2) Answer: 1. $$\frac{1}{2}\left|\begin{array}{ccc}{-2} & {-3} & {1} \\{3} & {2} & {1} \\{-1} & {-8} & {1}\end{array}\right|$$ $$\frac{1}{2}$$ (- 2(2 + 8) + 3(3 + 1) + 1(- 24 + 2)) = – 15 Area of ∆ ABC = 15. 2. The base AB is fixed and the third point is variable. Therefore we can choose any x coordinate and find y coordinate or vice versa. ⇒ – 2(2 – y) + 3(3 – 1) + 1(3y – 2) = 30 ⇒ – 4 + 2y + 6 + 3y – 2 = 30 ⇒ 5y = 30 ⇒ y – 6 Therefore point is(1, 6). Question 13. Find the inverse of the following Answer: (i) Let |A| = $$\left|\begin{array}{lll}{1} & {2} & {3} \\{0} & {2} & {4} \\{0} & {0} & {5}\end{array}\right|$$ = 10 C11 = 10, C12 = 0, C13 = 0, C21 = – 10, C22 = 5, C23 = 0, C31 = – 2, C32 = – 4, C33 = 2 (ii) Let |A| = $$\left|\begin{array}{ccc}{1} & {0} & {0} \\{3} & {3} & {0} \\{5} & {2} & {-1}\end{array}\right|$$ = -3 C11 = -3, C12 = 3, C13 = -9, C21 = 0, C22 = -1, C23 = -2, C31 = 0, C32 = 0, C33 = 3 (iii) Let |A| = $$\left|\begin{array}{ccc}{2} & {1} & {3} \\{4} & {-1} & {0} \\{-7} & {2} & {1}\end{array}\right|$$ = 2(-1 – 0) -1(4 – 0) + 3(8 – 7) = -3 C11 = -1, C12 = -4, C13 = 1, C21 = 5, C22 = 23, C23 = -11, C31 = 3, C32 = 12, C33 = -6 (iv) Let |A| = $$\left|\begin{array}{ccc}{1} & {-1} & {2} \\{0} & {2} & {-3} \\{3} & {-2} & {4}\end{array}\right|$$ = 1(8 – 6) + 1(0 + 9) + 2(0 – 6) = -1 C11 = 2, C12 = -9, C13 = -6, C21 = 0, C22 = -2, C23 = -1, C31 = 3, C32 = 3, C33 = 2 Question 14. Consider the system of equations 5x + 2y = 4, 7x + 3y = 5. If A = $$\left[\begin{array}{ll}{5} & {2} \\{7} & {3}\end{array}\right]$$, X = $$\left[\begin{array}{l}{\mathrm{r}} \\{y}\end{array}\right]$$ and B = $$\left[\begin{array}{l}{4} \\{5}\end{array}\right]$$ 1. Find |A| (1) 2. Find A-1 (2) 3. Solve the above system of equations. (1) Answer: 1. |A| = $$\left|\begin{array}{ll}{5} & {2} \\{7} & {3}\end{array}\right|$$ = 15 – 14 = 1. 2. Given, A = $$\left[\begin{array}{ll}{5} & {2} \\{7} & {3}\end{array}\right]$$ 3. X = A-1B ⇒ x = 2, y = -3. ### Plus Two Maths Determinants Six Mark Questions and Answers Question 1. (i) Let A be a square matrix of order ‘n’ then |KA| = …….. (1) (ii) Find x if $$\left|\begin{array}{cc}{x} & {2} \\{18} & {x}\end{array}\right|=\left|\begin{array}{cc}{6} & {2} \\{18} & {6}\end{array}\right|$$ (2) (iii) Choose the correct answer from the bracket. The value of the determinant $$\left|\begin{array}{ccc}{0} & {p-q} & {p-r} \\{q-p} & {0} & {q-r} \\{r-p} & {r-q} & {0} \end{array}\right|$$ is ….. (1) (iv) Consider $$\left|\begin{array}{ccc}{a} & {a+b} & {a+b+c} \\{2 a} & {3 a+2 b} & {4 a+3 b+2 c} \\{3 a} & {6 a+3 b} & {10 a+6 b+3 c}\end{array}\right|$$ (2) Answer: (i) If A be a square matrix of order n, then |KA| = Kn|A| (ii) $$\left|\begin{array}{cc}{x} & {2} \\{18} & {x}\end{array}\right|=\left|\begin{array}{cc}{6} & {2} \\{18} & {6}\end{array}\right|$$ ⇒ x2 – 36 = 0 ⇒ x2 = 36 ⇒ x = ±6. (iii) (c) 0 (since the given determinant is the determinant of a third order skew symmetric matrix) = a [7a2 + 3ab – 6a2 – 3ab] = a(a2) = a3 Question 2. (i) Let $$\left|\begin{array}{lll}{1} & {3} & {2} \\{2} & {0} & {1} \\{3} & {4} & {3} \end{array}\right|$$ = 3, then what is the value of $$\left|\begin{array}{lll}{1} & {3} & {2} \\{4} & {0} & {2} \\{3} & {4} & {3}\end{array}\right|$$ = ? and$$\left|\begin{array}{lll}{6} & {7} & {6} \\{2} & {0} & {1} \\{3} & {4} & {3}\end{array}\right|$$ = ? (2) (Hint: Use the properties of determinants) (ii) Using properties of determinants show that (4) $$\left|\begin{array}{ccc}{1+a} & {1} & {1} \\{1} & {1+b} & {1} \\{1} & {1} & {1+c}\end{array}\right|=a b c\left(1+\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)$$ Answer: (ii) Taking ‘a’ from R1, ‘b‘ from R2,’C’ from R3 Question 3. If A = $$\left[\begin{array}{ccc}{2} & {-3} & {5} \\{3} & {2} & {-4} \\{1} & {1} & {-2}\end{array}\right]$$ 1. Find |A| (1) 2. Find adj.A. (2) 3. Solve 2x – 3y + 5z = 11, 3x + 2y – 4z = -5, x + y – 2z = -3 (3) Answer: 1. A = $$\left[\begin{array}{ccc}{2} & {-3} & {5} \\{3} & {2} & {-4} \\{1} & {1} & {-2}\end{array}\right]$$ |A| = 2 × 0 + 3x – 2 + 5 = -1. 2. Co.factor A 3. Given i.e; AX = B ⇒ X = A-1 B Question 4. Let A = $$\left[\begin{array}{ccc}{1} & {-1} & {1} \\{2} & {1} & {-3} \\{1} & {1} & {1}\end{array}\right]$$ 1. Is A singular? (1) 2. Find adj A. (2) 3. Obtain A-1 (1) 4. Using A-1 solve the system of equations x – y + z = 4, 2x + y – 3z = 0, x + y + z = 2 (2) Answer: 1. A = $$\left[\begin{array}{ccc}{1} & {-1} & {1} \\{2} & {1} & {-3} \\{1} & {1} & {1}\end{array}\right]$$ ⇒ |A| = 4 + 5 + 1 = 10 ≠ 0 A is non singular matrix. 2. Cofactor A 3. A-1 = $$\frac{1}{10}$$ $$\left[\begin{array}{ccc}{4} & {2} & {2} \\{-5} & {0} & {5} \\{1} & {-2} {3}\end{array}\right]$$ 4. Given, AX = B ⇒ X = A-1 B ⇒ x = 2, y = -1, z = 1. Question 5. Solve the following system of linear equations. 1. x + y + z = 3, y – z = 0, 2x – y = 1 (6) 2. 5x – 6y + 4z = 15 , 7x + 4y – 3z = 19, 2x + y + 6z = 46 (6) 3. x + 2y + 5z = 10, x – y – z = -2, 2x + 3_y-2 = -11 (6) Answer: 1. Let AX = B Where A = $$\left[\begin{array}{ccc}{1} & {1} & {1} \\{0} & {1} & {-1} \\{2} & {-1} & {0}\end{array}\right], X=\left[\begin{array}{c}{x} \\{y} \\{z}\end{array}\right], B=\left[\begin{array}{l}{3} \\{0} \\{1}\end{array}\right]$$ |A| = 1(0 – 1) – 1(0 + 2) + 1(0 – 2) = -5 C11 = -1, C12 = -2, C13 = -2, C21 = -1, C22 = 3, C23 = 3, C31 = -2, C32 = 1, C33 = 1 2. Let AX = B, Where A = $$\left[\begin{array}{ccc}{5} & {-6} & {4} \\{7} & {4} & {-3} \\{2} & {1} & {6}\end{array}\right], X=\left[\begin{array}{c}{x} \\{y} \\{z}\end{array}\right],B=\left[\begin{array}{c}{15} \\{19} \\{46}\end{array}\right]$$ |A| = 5(24 + 3) + 6(42 + 6) + 4(7 – 8) = 419 C11 = 27, C12 = -48, C13 = -1, C21 = -1, C22 = 22, C23 = -17, C31 = 2, C32 = 43, C33 = 62 3. Let AX = B $$\text { Where } A=\left[\begin{array}{ccc}{1} & {2} & {5} \\{1} & {-1} & {-1} \\{2} & {3} & {-1} \end{array}\right], X=\left[\begin{array}{c}{x} \\{y} \\{z}\end{array}\right], B=\left[\begin{array}{c}{10} \\{-2} \\{-11}\end{array}\right]$$ |A| = 1(4) – 2(1) + 5(5) = 27 C11 = 4, C12 = -1, C13 = 5, C21 = 17, C22 = -11, C23 = 1, C31 = 3, C32 = 6, C33 = -3 ⇒ x = -1, y = -2, z = 3. Question 6. If f(x) = $$\left[\begin{array}{ccc}{\cos x} & {-\sin x} & {0} \\{\sin x} & {\cos x} & {0} \\{0} & {0} & {1}\end{array}\right]$$ (i) Find f(-x) (2) (ii) Find (f(x)]-1 (2) (iii) Is |f(x)]-1 = f(-x)? (2) Answer: (ii) |f(x)| = $$\left[\begin{array}{ccc}{\cos x} & {-\sin x} & {0} \\{\sin x} & {\cos x} & {0} \\{0} & {0} & {1}\end{array}\right]$$ = cos x (cos x) + sin x (sin x) = 1 ≠ 0 Therefore , [f(x)]-1 exists. The cofactors are as follows. C11 = cos x, C12 = -sin x, C13 = 0, C21 = sin x, C22 = cos x, C23 = 0, C31 = 0, C32 = 0, C33 = 1 Since, |f(x)|= 1 (iii) Yes. From (1) and (2) we have, [f(x)]-1 =f(-x). Question 7. (i) Choose the correct answer from the bracket. If A = $$\left[\begin{array}{cc}{2} & {3} \\{1} & {-2}\end{array}\right]$$ and A-1 = kA, then the value of ‘k’ is (a) 7 (b) -7 (c) $$\frac{1}{7}$$ (d)$$-\frac{1}{7}$$ (1) (ii) If A = $$\left[\begin{array}{ccc}{1} & {-1} & {1} \\{2} & {-1} & {0} \\{1} & {0} & {0} \end{array}\right]$$, (a) A2 (2) (b) Show that A2 = A-1 (3) Answer: C11 = 0, C12 = 0, C13 = 1, C21 = 0, C22 = -1, C23 = -1, C31 = 1, C32 = 2, C33 = 1 Question 8. ‘Arjun’ purchased 3 pens, 2 purses, and 1 instrument box and pays Rs. 410. From the same Shop ‘Deeraj’ purchases 2 pens, 1 purse, and 2 instrument boxes and pays Rs.290, while ‘Sindhu’ purchases 2pens, 2 purses, 2 instrument boxes and pays Rs. 440. 1. Translate the equation into system of linear equations. (2) 2. The cost of one pen, one purse and one instrument box using matrix method. (4) Answer: 1. Let The price of one pen is Rs.x, one purse is Rs.y and one instrument box be Rs.z 3x + 2y + z = 410; 2x + y + 2z =290; 2x + 2y + 2z = 440(1) 2 mts. 2. The system can be represented by the matrix equation AX = B C11 = -2, C12 = 0, C13 = 2, C21 = -2, C22 = 4, C23 = -2, C31 = 3, C32 = -4, C33 = -1 Hence the cost one pen is Rs.20, one purse is Rs. 150 and one instrument box is Rs. 50. Question 9. If A = $$\left[\begin{array}{ccc}{2} & {-3} & {5} \\{3} & {2} & {-4} \\{1} & {1} & {-2}\end{array}\right]$$ 1. Find A-1 (3) 2. Using it solve the system of equations 2x – 3y + 5z = 16, 3x + 2y – 4z = -4, x + y – 2z = -3 (3) Answer: 1. A = $$\left[\begin{array}{ccc}{2} & {-3} & {5} \\{3} & {2} & {-4} \\{1} & {1} & {-2}\end{array}\right]$$ ⇒ |A| = 0 + 3x – 2 + 5 = -1 2. Given AX = B ⇒ X = A-1B ⇒ x = 2, y = 1, z = 3. Question 10. Consider the following system of equations x + y + 3z = 5, x + 3y – 3z = 1, -2x – 4y – 4z = -10 (i) Convert the given system in the form AX = B (1) (ii) Find A-1 (3) (iii) Hence solve the system of equations. (2) Answer: (ii) i.e; AX = B, ⇒ X = A-1 B ⇒ |A| = -24 + 10 + 6 = -8 (iii) X = A-1B = $$-\frac{1}{8}$$ $$\left[\begin{array}{l}{-8} \\{-8} \\{-8}\end{array}\right]$$ ⇒ x = 1, y = 1, z = 1. Question 11. Solve the following system by equations by matrix method x + 2y + 5z = 10; x – y – z = -2; 2x + 3y – z = -11. Answer: x + 2y + 5z = 10; x – y – z = -2; 2x + 3y – z = 11 ⇒ x = -1, y = -2, z = 3. Question 12. If A = $$\left[\begin{array}{ccc}{3} & {-2} & {3} \\{2} & {1} & {-1} \\{4} & {-3} & {2}\end{array}\right]$$ 1. Find |A| (1) 2. Find A-1 (3) 3. Solve the linear equations 3x – 2y + 3z = 8; 2x + y – z = 1; 4x – 3y + 2z = 4 (2) Answer: 1. |A| = $$\left[\begin{array}{ccc}{3} & {-2} & {3} \\{2} & {1} & {-1} \\{4} & {-3} & {2}\end{array}\right]$$ = 3(2 – 3) + 2(4 + 4) + 3(- 6 – 4) = -17. 2. |A| ≠ 0, hence its inverse exists. A-1 = $$\frac{1}{|A|}$$adj A C11 = -1, C12 = -8, C13 = -10, C21 = -5, C22 = -6, C23 = 1, C31 = -1, C32 = 9, C33 = 7 3. The given system of linear equations is of the form ∴ We have, x = 1, y = 2, z = 3. Question 13. if $$\left[\begin{array}{cc}{2} & {5} \\{-3} & {7}\end{array}\right] \times A=\left[\begin{array}{cc}{17} & {-1} \\{47} & {-13}\end{array}\right]$$ then (i) Find the 2 × 2 matrix A. (3) (ii) Find A2. (1) (iii) Show that A2 + 5A – 6I = 0, where I is the identity matrix of order 2. (2) Answer: ## Plus Two English Textbook Answers Unit 5 Chapter 3 Crime and Punishment (Short story) Kerala State Board New Syllabus Plus Two English Textbook Answers Unit 5 Chapter 3 Crime and Punishment Text Book Questions and Answers, Summary, Notes. ## Kerala Plus Two English Textbook Answers Unit 5 Chapter 3 Crime and Punishment (Short story) Read And Respond (Text Book) Question 1. Why did the boy try to fool the teacher by repeating his mistake? Answer: The boy tried to fool the teacher by repeating his mistake because he did not want to continue with his studies. He was interested in playing and not studying. Question 2. Why did the parents give the boy intensive coaching in Mathematics? Answer: The parents gave the boy intensive coaching in Mathematics because they wanted him to score 50 in Mathematics and thus get a double promotion to the first form. Question 3. How does the teacher react when the boy repeated the mistake several times? Answer: The teacher slapped the boy hard on his cheek when he repeated the mistake several times. Question 4. What is the boy’s response when the teacher slapped him on his cheek? Answer: The boy gazed at the teacher for a moment and started crying. Question 5. Why does the teacher ask the boy not to tell the incident to his mother? Answer: The teacher asks the boy not to tell the incident to his mother because the mother would get angry and dismiss him from work. Question 6. How do the parents consider the boy? Answer: The parents consider the boy a little angel. He was their only child and they gave him a lot of love. Question 7. What facilities do the parents provide to the boy? Answer: They built him a nursery, bought him expensive toys, fitted up miniature furniture sets, gave him a small pedal motor car to move about in the garden. His cupboard was filled with chocolates and biscuits which he could eat as he wanted. Question 8. Why do the parents give half an hour’s class on child psychology to the teacher every day? Answer: The father had written a thesis on infant psychology for his M.A. The mother had studied a good deal of it for her B.A. It seemed they wanted him to treat the boy as if he was made of thin glass. The parents thought that no prohibition or repression should affect the boy’s mind. If you make restrictions and repressions, you will damage the child for life. Question 9. Why does the teacher consider the boy a gorilla? Answer: The teacher considers the boy a gorilla because he is very mischievous. He does not want to study and he disobeys instructions. The parents thinkthe boy is a little angel, but the teacher knows he is a gorilla difficult to teach and manage. Question 10. How does the boy compel die teacher to act as a station master? And what duty does he assign to the teacher? Answer: The boy compels the teacher to act as a station master by threatening to tell the slapping incident to his parents. His duty was to blow the whistle when the train reached his station and ask the train driver to stop the train as there are many people who have bought tickets. Question 11. When is the teacher relieved of the role of the station master? Answer: The teacher is relieved of the role of the station master when the train refused to move. The boy handed it to the teacher and told him to repair it. The teachertumed it around in his hand and said he did not know anything about it. Question 12. Why does the teacher become desperate? Answer: The teacher becomes desperate because he can’t make the train work. He was absolutely non-mechanical and he does not know what to do to make the train move. Question 13. How does the teacher become tired? Answer: The teacher becomes tired because he had done six hours of teaching at school during the day. He had lost his breath. Question 14. Why does the teacher decide to reveal the matter to the parents? Answer: The teacher decides to reveal the matter to the parents because he is tired of the blackmailing by the boy. It is better to tell the truth to the parents and accept whatever punishment they give than stand the blackmailing by the boy. Question 15. Why does the boy become so annoyed and slink behind his parents? Answer: The boy becomes so annoyed and slinks behind his parents when his father asked the teacher how the boy was preparing for the test in arithmetic. #### Crime and Punishment (Story) Edumate Questions & Answers Question 1. When the boy obstinately said the same he felt as if his finger were releasing the trigger. He reached across the table, and delivered a wholesome slap on the youngster’s cheek. What is your opinion about the teacher’s behaviour? What could the teacher have done instead? Express your views in a paragraph. Answer: The teacher was wrong in slapping the boy on the cheek. It was a hard slap making the boy’s cheek red. Instead of slapping the boy, he could have asked him a different question or said some interesting things to bring the boy back into the study-mood. Corporal punishment to children is strictly prohibited in many countries. By giving corporal punishment you make the students hate their studies. Studies are done better when the students have a desire to study. I think the best way to teach is to tickle the curiosity in children and motivate them. Let them leam things because they want to learn them and not because they are forced or punished. Question 2. Imagine that the teacher decides to confess his crime to the boy’s parents after the class. What will the teacher say? Draft a confession statement for the teacher. Answer: Today something bad happened. You had told me that your son should get 50 marks in the class test forgetting a double promotion. I was trying hard to improve his arithmetic. I taught him the table of 16 up to 10.1 was checking if he remembered it. I asked him what is 16 x 3. He said 24.1 corrected him and made him say 48. Again I asked him and again he said 24. I thought he was trying to make me a fool by deliberately giving me the wrong answer each time I asked him. I don’t know what came over me. I suddenly lost my temper and I slapped him on the cheek. I remember your advice to me to treat your son as if he is made of thin glass. I forgot all that for a moment. I am sorry. But what I did was for the better future of your son and to make your dream about him come true. Now it is up to you to decide what to do with me. Question 3. Read the following headlines. 58 percent children suffer from ailment due to heavy school bags Heavy school bags lead to back pain in children Thousands of small children are reeling physically under the pressure of studies and heavy bags like the boy in the story ‘Crime and Punishment’. Heavy school bags is a matter of great concern to parents and children. You decide to arouse a public opinion on this matter via a blog entry. How could it be? (6 Mark) Answer: Children Are Not Load-Carrying Mules. Vijayan is 10 year old boy studying in Class V. He has been complaining of severe back pain. He was taken to the hospital. A scan showed that his backbone was bent badly. How won’t it bend? He is carrying 15 kg of books, tiffin carrier loaded with lunch, water and umbrella in his backpack every day, walking to and from school, one kilometre away. A Surgery had to be carried out. The doctor told his parents not to let him carry such weights on his back again! Why do small children carry so much of weight in their backpacks? I remember my granddad telling me that when he was a primary school student he had only a slate, a couple of text books and notebooks to carry apart from his tiffin carrier. He drank water from the school well. Thus he carried less than one kg to school. Today when we see school children going to school in the morning, we are reminded of caravans in which we see camels or mules loaded with heavy things on their backs. There is no logical reason why small children should be made into mules. Can’t some of the books be left in the school locker? Can’t they get drinking water in the school itself? I think it is high time we thought of methods of reducing the weight of the bd’c^ack carried by small children. Somebody jocularly remarked that today’s children carried knowledge on their backs, whereas the children of the earlier generations carried knowledge in their brains. There is a lot of truth in the statement. Parents should ensure that they don’t let their children carry heavy loads on their backs. In the long run these children will become sick with many problems affecting their vertebral column. Let’s all join hands to make the burden of the school children lighter! Question 4. Imagine that a debate was held in your class on the topic ‘Corporal Punishment Hampers Child’s Growth.’ The following points were presented against the topic. 1. Corporal punishment is necessary for maintaining discipline. 2. Corporal punishment reinforces positive behaviour. 3. Corporal punishment instils respect towards teachers. 4. Corporal punishment is more effective than any other method. Write four arguments for the topic. Answer: 1. Corporal punishment makes the student hate the subject and also the teacher who teaches it. 2. Corporal punishment is a negative influence. Things learned through such influences are easily forgotten. 3. Corporal punishment is violation of children’s right. Children are to be taught through positive ways and not by inflicting pain on them. 4. Corporal punishment breeds violence. When a student is beaten, there is a tendency in him to beat others who go against his wishes. Violence breeds violence. Question 5. Imagine that an extempore speech competition is conducted in your school. You are asked to speak on the topic ‘Indian Education System’ .You are given three minutes for preparation. You decide to jot down a few points in your notepad. What will you write? List out the points. Answer: Indian Education System • Still based on ‘talk and chalk’ method. • Overcrowded classrooms. • No light and fan in classrooms. • Student-Teacher ratio not good at all. • Stress is on learning by rote. • Book-learning is emphasized without any emphasis on practical work. • In the examination only memory is tested. • Many schools lack laboratories and libraries. • Many schools lack recreational facilities. • Many classrooms are not hygienic; inadequate toilet facilities. Question 6. A panel discussion on the topic ‘Student Rights and Responsibilities’ is conducted in your class. You are asked to initiate the discussion. How would you introduce the topic? Prepare an introductory speech. Answer: Student Rights And Responsibilities: Respected Principal, dearteachers and students, In the Panel Discussion today, the topic is the rights and responsibilities of the students. Rights and responsibilities are the two sides of the same coin. Rights involve responsibilities and responsibilities bring in rights. Students have many rights and corresponding responsibilities. I will not go into the details of the rights and responsibilities of students as they will be done by the panel members. But I will mention a few of them as a starting point. I believe the primary right of the students is the right to be taught properly. They come to the school with the main intention of learning. So they have a right be taught in a way they understand what is being taught. Students have a right to have recreational and sports and games facilities. There is a well-known Latin saying, “mens sana in corpora sano” which means “a healthy mind in a healthy body.” “All work and no play makes Jack a dull boy.” Students should have playgrounds and material for various games and sports. Then only they can build healthy bodies. This is especially the case with students in their teens. Students should have a right to assemble and air their views. Thus they have a right for association. They have a right to express their opinions on the various things going on in the campus and the management should be willing to listen to their views. Students have the responsibility to study well. They should respect their teachers and their classmates. They have the responsibility to keep the campus clean. They should take care of the school properties and no wilful damage should be done. They have the responsibility to pay any fee or charge that is mandatory. They have the responsibility to strictly adhere to the code of conduct for students. They have the responsibility of not doing any un-student like activities in the school, like smoking, drinking alcoholic beverages and taking drugs. They have the responsibility not to bring in politics into the school. They have the responsibility of being morally upright. They have the responsibility to work hard and achieve their goals in life. Well, students have many rights and responsibilities and they do not end with the ones I have mentioned. Our panel members will enlighten us more about them. I am sure we will have a fruitful discussion. Thank you, all! Question 7. The teacher in the story ‘Crime and Punishment’ is very much excited after winning the faith of the small boy. He narrates the incident to one of his friends. What would he say? Prepare the narration for him. Answer: Teacher: You know, today something very funny happened in the nursery. I am teaching a devil of boy there. The only reason I teach him is the Rs.30 his parents pay me every month. For 30 bucks I have to suffer for 3 hours every evening. First, his parents lecture me on child psychology. The boy’s father had written a thesis in infant psychology for his M.A. The mother had studied a good deal of it for her B.A. So, both of them tell me almost the same things day after day. They want me to treat their son as if he is made of very thin glass. What the boy needs is beating and not cajoling. He is not a boy but a gorilla. My God! You have never seen such a rascal. Today I asked him the result of 16 multiplied by 3.1 had taught him the multiplication of 16 up to 10. I am sure he knew the right answer. But he said 24.1 corrected him and asked him again for the correct answer. With a grin, the gorilla says 24. I lost my temper. I slapped him on his cheek, leaving a red mark there. He then wanted me to stop teaching and play with him, pretending as a station master while he drove his train. I refused. He threatened and said he would run to his parents and show the mark on his cheek. That would be the end of my 30 bucks which I heed badly. So reluctantly I played with him. Fortunately the train stopped. And then the devil wanted me to tell stories. I went on saying the usual stories – the bison and the tiger, AN Baba and the 40 Thieves. He wanted me to repeat the bison-tigerstory again. When I said no, he ran home. I ran behind him. When the parents asked why we were running I told them that I was trying to keep the spirits of the boy up by doing this exercise after his strenuous learning. Then the father asked me about the test. When the boy heard the word test, he went and stood behind his father indicating to me I should support him. I said he was doing well, and I was sure that boy will not tell his parents about the slapping I gave him. My extra income is safe for the moment. Question 8. Based on the story ‘Crime and Punishment’ write an expository essay on the topic ‘Role of Parents in Moulding the Character of Children.’ Answer: Role of Parents in Moulding the Character of Children Moulding their children’s character is a great concern of all parents. Parents are constantly doing something or other to make their child do better in studies, inculcate better discipline, excel in sports, learn social interaction and various other aspects depending on their own vision and capabilities. Whether they are aware of it or not they are constantly shaping their child as moulding is an integral part of parenting. Parenting basically has to do with training, disciplining, moulding and at times forcing children to live as parents dictate. Forcing a child to adapt to what they think is right or what they feel the child should be doing is forceful parenting. Forceful parenting often does more damage to their children than it does good. It can demolish self-confidence and destroy the imagination of children. Parents should strive to ensure that their children learn to experience and express themselves as free human beings. Now-a-dayswe have parents who, even before the child is one year old, decide to turn him/her into another Virat Kohli or Deepika Padukone. Most of the problems with adolescents can be traced back to an early age when they learned they were to just follow orders. Children who have to comply rigidly with what is expected of them, develop neither their own vision nor accountability. When not nurtured, their natural lights dim and they just follow their peers or the heroes that are shown to them by the entertainment media. Some parents, on the other hand, are proud that their children are quiet and polite and that they have done their job very well. They don’t realize that their children are not just quiet but complacent. These children behave that way probably because they have stopped to think. Guiding your child to achieve his/ hertrue potential is good parenting. Real moulding is when your child shows some abnormal behaviour that is either against the norms of society oris affecting his overall growth and development and you correct that. The question that bothers most parents is: “What is more important: to shower a child with love and let Nature take its course or to provide intellectual stimulation?” Tfieiatest theory maintains that the one complements the other. In the past, it was thought that love could develop a child and compensate for lack of intellectual stimulation. Today we know that to develop a child’s mind and mould his personality mental stimulation initiated by the parents is important. The bulk of the responsibility for moulding their children’s character rests with the parents. Ideally, parents should rouse their curiosity by giving them plenty of information. When they grow up, they feel free to ask questions about all kinds of things in their environment as their curiosity would have been developed to a keen edge. Parents directly influence their child’s development and behaviour. They must teach their children the importance of honesty, truth, kindness, generosity, hard work and polite behaviour. There has been a controversy of heredity versus environment. But it is feltthat heredity, environment and good parenting make the children ideal citizens useful for themselves, their families, their society and humanity at large. Thus, parents have a big role to play in the formation of their children’ character. Question 9. a) Do you think the title ‘Crime and Punishment’ is an apt one? Justify your views. b) Write an alternative title for the story. Answer: a) I think the title “Crime and Punishment” by R.K. Narayan is an apt one forthe story. There is crime and then there is punishment. The boy does the crime of repeating the same mistake wilfully and he gets slapped as punishment. Slapping is the crime by the teacher and he gets punishment from the boy. That is why he has to act as a station mater and tell him so many stories ad run after him, all against his will. In fact there is a world famous novel by the same name by the Russian author Fyodor Dostoyevsky. Narayan must have copied the title. But in Dostoyevsky’s novel, the crime is murder and not the small mishiefs in R.K. Narayan’s story. b) The Plight of a Poor Teacher/The Mischievous Imp and the Poor Teacher Question 10. The story ‘Crime and Punishment’ deals with the relationship between a teacher and a small boy. What impression do you get about the teacher? Sketch his character. Answer: The teacher in the story “Crime and Punishment” by R.K. Narayan is a hardworking man. He teaches 6 hours in the school and then he comes to teach the small boy in the nursery for just 30 rupees a month. He has to work for three hours in the nursery teaching a gorilla of a child. This shows the teacher is very poor. Otherwise he would not come to teach such a mischievous imp after his normal school hours. The teacher suffered at the hands of the parents also. Every day he had to listen to the lectures of the parents on child psychology for half an hour. The father had written a thesis on infant psychology for his M.A. The mother had studied a good deal of it for her B.A. So, both lectured to him on the same lines. It seemed that the parents of the boy thought he was made of thin glass. They pampered him a lot and they wanted the teacher also to be very kind to the boy and not to annoy him in any way. The teacher found it hard to manage the boy. The boy had a lot of love and money. His parents built the nursery for him. They bought him expensive toys. They even gave him a small pedal motor to move about in the garden. His cupboard was filled with chocolates and biscuits which he could eat whenever he wanted. He was a highly pampered, spoilt child. The teacher could lose his temper when tempted too much. He slaps the boy because the boy persisted in making the same mistake in spite of the corrections so many times. The hard slapping made a red mark on the cheek of the boy. The boy used that mark to blackmail the teacher. He teacher had to play with the boy acting as a station master. Then the train stops running and the boy wants him to repair it. But the teacher is not at all mechanical minded and he can’t do that. Then the boy makes him tell stories. He tells the story of the tiger and the bison and the story of AN Baba and 40 thieves. The boy wants to hear the story of the tiger and bison again. When the teacher refuses the boy runs home, the teacher in hot pursuit. The teacher has good presence of mind. When the father asks why they are running about, the teacher says they are just playing about to keep up their spirits. The teacher can lie if there is a need! Poor teacher! He has to suffer so much for getting an extra amount of Rs.30 per month! I think he represents many teachers in our society who do not get a decent salary and have to find others ways of making both ends meet. Question 11. In ‘Crime and Punishment’ problems start when the teacher slaps the boy. In your opinion, what are the impacts of that punishment on the boy? Write a paragraph. Answer: The first impact of the slap was that the boy burst into tears. He is not used to getting such slaps as he is a much pampered boy at home. When teacher tries to make him stop crying and behave like a soldier, the boy retorts saying that a soldier would shoot with a gun if he was hit. The next impact is that the boy becomes stubborn and he wants to blackmail the teacher. He wants the teacher to stop teaching and play with him with a toy train. The teacher would be the station master. First the teacher refuses and then the boy threatens him by saying he would report the slapping to his parents. The teacher has no way but to please the boy. Soon the train breaks down. And then boy wants to teacher to tell him stories. He tells the stories of the tiger and the bison and the story of Ali Baba and 40 Thieves. The boy wants to the story of the tiger and the bison repeated. When tbe teacher refuses the boy again threatens him and runs home. The teacher runs behind to catch him. It is obvious that the slapping has no positive effect on the boy. It has only made him more stubborn. Question 12. “Good night sir, we finished our lessons early and I was just playing about with the child something to keep up his spirits you know,” says the teacher in the story ‘Crime and Punishment’. Here the teacher suggests playing as a mode of relaxation for his student. What are the other methods by means of which students can keep up their spirits? Prepare a write-up on the topic ‘Need for Relaxation and Recreation in Academics.’ Answer: Need for Relaxation and Recreation in Academics There is a well-known Latin saying, “mens sana in corpora sano” which means “a healthy mind in a healthy body.” “All work and no play makes Jack a dull boy.” Students should have relaxation and recreation in their academics. There should be playgrounds and material for various games and sports. Then only they can build healthy bodies. This is especially the case with students who are very young. In young children the attention span is very short. You can’t drill into their minds facts, figures and formulae for a long time. Soon they get bored and nothing will entertheir brain. There are many ways to keep the spirits of the students up. One of the ways is making the children sing in the class. Another way is telling stories. Quizzes and Puzzles can be used for entertainment and relaxation. Things like Antakshari can help. Word building is useful. Asking for synonyms and antonyms is a good pastime. Board games are an excellent way of relaxation. Taking the children out for small walks helps. Short films can be shown to make the children relaxed. Innovative teachers can think of many more ways to give relaxation and recreation to students. Question 13. “He was their only child, they had abundant affection and ample money they filled up his cupboard with all kinds of sweets and biscuits, and left it to his good sense to devour them moderately. They believed a great deal in leaving things that way.” What does the above excerpt tell us about the attitude of the boy’s parents? Are they right in the method of bringing up their only child? Express your opinion in a paragraph. Answer: The excerpt shows that the parents were too indulgent towards their son. They are not right in the method of bringing up their child. A child brought up that way is unable to cope with adverse circumstances. When they have to face a little physical or mental discomfort, they completely lose their mental balance. It is such children that often commit suicide. We hear so many stories of children killing themselves. One hangs himself because he failed in the exam. Another jumps into the river and kills himself because a teacher shouted at him. A third jumps from the 4th floor because he was asked by the Principal to bring his parents as he was playing truant. Many children become depressed when faced with even small problems. I think children should be trained to face problems of life boldly. Problems are bound to come in life. So we need children who can stand up and say “Come what may. I’ll see what I can do!” By giving their abundant love and ample money and filling his cupboard with all types of delicacies for him to eat at will is definitely pampering him too much and they are making him unfit to face the challenges of the modern world. Question 14. As part of a campaign conducted in connection with the ‘General Protection Mission’, an essay competition was conducted by the Education Department. The topic is ‘Modern Day Classrooms- Expectations and Realities’. Prepare an essay to be sent to the department. Answer: Modern Day Classrooms – Expectations And Realities. It is a pity that even though we got independence 70 years ago, our educational system has not improved much from the days of the British rule here. We still practise the old talk and chalk method of teaching in congested classrooms with just a blackboard and some pieces of chalk and a few benches and desks for the students. The classrooms are crowded, not properly ventilated’and most classrooms do not have lights and fans. Sitting in the classrooms becomes a boring affair and the atmosphere there is not at all conducive to learning. These things have to change. We have to improve our classrooms to international standards. Then only the teaching and learning process will become efficient and enjoyable. Teaching and learning should become an enjoyable activity by the teachers as well as the students. To motivate them we should ensure that the classroom offer a conducive atmosphere. To improve the teaching-learning process, we need smart classrooms. Smart Classrooms are technology enhanced classrooms that foster opportunities for teaching and learning by integrating learning technology, such as computers, specialized software, audience response technology, assistive listening devices, networking, and audio/visual capabilities. Such classrooms will help the students to feel fully engaged in the lessons and understand them better. Science and technology are growing at mind-boggling speed and this growth should be reflected in our classrooms. Then we have to improve the student-teacher ratio. In some of our classrooms there are often more than 60 students. How can a teacher teach 60 or more students efficiently? He can’t give individual attention to the students. All students are not equally intelligent or motivated. So the student-teacher ratio should be such that all students can get individual attention. Another thing is changing our teaching methods. We do not have proper laboratories. Even chemistry, and physic and biology are taught in ordinary classrooms through the lecture method. Students learn things by doing, especially in science subjects. But we still teach by saying “Suppose this is a test tube. Suppose I am pouring some sulphuric acid into it. Suppose I put some ………” and it goes on like that. Students hardly,learn by such suppositions. Let the students see the things and practically carry out the experiments. And then they will learn. Practice makes perfect. For teaching language efficiently, language laboratories are essential. Languages may have different phonemes. In English, for example, we have 44 phonemes, of which 24 are consonant, 12 vowels and 8 diphthongs. Some of these phonemes do not exist in Malayalam. So they ought to be taught very carefully. In English /v/ and /w/ are two different phones. So are /s/ and /z/. But we Malayalees pronounce them as if there is no difference. For us ‘veil’ and ‘wail’ have no difference in pronunciation. So are ‘vine’ and ‘wine’. So students should be taught to articulate /v/ and /w/ properly. M is a labio-dental sound where was /w/ is a bilabial. The confusion between /s/ and Izl also should be corrected. For that we need a language lab. The problem is more when it comes to certain vowels in English. Smart classrooms are a necessity of the times. Well lit, properly ventilated classrooms with enough space for each student are essential for learning. In such classrooms, teaching and learning become a pleasant and efficient affair. Question 15. Read the following excerpt and answer the questions that follow. They lectured to him every day on their theories, and he got more and more the feeling that they wanted him to deal with the boy as if he were made of thin glass. He had to pretend that he agreed with them, while his own private view was that he was in charge of a little gorilla. a) Who does ‘they ‘refer to in the passage? b) What mood does the expression ‘as if he were made of thin glass express? a. indifference b. rudeness c. carefulness d. contempt c) Express your views on the attitude of the teacher. Answer: a) The boy’s parents. b) contempt c) The parents loved the boy too much and pampered him. They wanted the teacher also do the same. The teacher pretended as if he agreed with the parents. But he knew that the boy whom he had to teach was a mischievous imp, a monster, a gorilla, who needed caning and not cajoling. Question 16. The interjection ‘as if means ‘in a manner suggesting’ or ‘in mimicry of. Read the following passage from the story ‘Crime and Punishment’ and rewrite the sentences using ‘as if. The child’s parents lectured to the teacher everyday on their theories like experts in Psychology. They wanted the teacherto deal with the child like delicate glass. But, in truth, the boy behaved like a gorilla. Answer: The child’s parents lectured to the teacher every day on theories as if they were experts in psychology. They wanted the teacherto deal with the child as if he were a piece of delicate glass. But in truth the boy behaved as if he were a gorilla. Question 17. Imagine that your class is going to dramatise the story ‘Crime and Punishment’. You are asked to write a script for the extinct given below which forms the beginning of the play. ‘What is sixteen and three multiplied?”asked the teacher…….. “Twenty four,” with, as it seemed to the teacher, a wicked smile on his lips at the mention of “Twenty four, “the teacher felt his blood rushing to his head…….. he reached across the table, and delivered a wholesome slap on the youngster’s cheek… “I will tell them,” sobbed the boy. Prepare the script. Hints: (characters-stage setting-dialogues-gestures etc.) Answer: (A small classroom. There is a small desk and a small chair for a small boy to sit and learn. There is a chair for the teacher. A small blackboard is fixed on to the wall near the teacher. The teacher, a man of around 36, is standing with an Arithmetic Text Book prescribed for Form I. A boy is sitting lazily in the class. There is a fan working. Its noise can be heard. A tuition class is going on.) Teacher: What is 16 and 3 multiplied? Boy (smiling wickedly): 24 Teacher (His face shows anger): How many times did I tell you that 16 x 3 is 48? (Pointing his finger at the boy) Do you get it? Boy: (Nodding his head vigorously) Yes! Yes! Teacher: Okay! What is 16 and 3 multiplied? Boy: (With a mischievous smile): 24 Teacher (Very angry.) Yes, 24! You, gorilla! (He rushes to the boy in a rage and gives him a hard slap on the boy’s cheek. The boy never expected such a thing to happen.) Boy: Aiyo! Aiyo! My teeth are broken, (caressing his cheeks) Oh My God! Oh My God! I will tell my parents you slapped me. I will tell my parents. (He cries loudly. The teacher is confused and he is trying to calm down the boy.) Question 18. In the story ‘Crime and Punishment’ we come across the rift among the teacher, student and parents. Consider this story as a satire on the modern education system and prepare a write-up in about 100 words. Answer: The rift we see among the teacher, student and parents in the story “Crime and Punishment” by R.K. Narayan is typical of the modern education system. Almost all parents, especially in Kerala, want even their below-average students to become doctors and engineers. The parents have high expectations from their children. The children want to enjoy their life with all the modern gadgets available to them. Teachers want to make money. Look at the number of coaching centres we have! What is the only aim of the so-called coaching centres? Students are forced to go there by the ambitious parents. So we have a vicious circle. Teachers tlo not do their real work in their regular class hours because they want to ‘work’ in the tuition centres. In the Exams of 2017 we saw how Coaching Centres and people in charge of setting Examination Question Papers collude to make money, playing with the lives of children. The modern education system especially in Kerala is in a mess. Education has become a major industry in Kerala. The result? Many students commit suicide as they can’t cope with the strain of studies. We should change all that. The earlier, the better. Question 19. Imagine that a servant in the boy’s house is a silent witness to the troubles created by the boy in the class. He feels sad at the plight of the teacher who is helpless in disciplining the boy. One day, he meets the boy’s parents and describes what has been going on in the evening class. What would be his comments? Write a paragraph of about four sentences. Answer: Sir and Madam, I want to tell you something about your son’s evening class. I don’t think he studies much there. He makes a fool of the teacher. The other day I saw how he forced the teacher to play with him. As he was playing with the train, he wanted the teacher to become the station master. The teacher had to agree because otherwise the boy would complain to you about the teacher and the poor teacher would lose his job here. When the train stopped, he asked the teacher to tell him stories. He told the story of the tiger and the bison and then the story of Ali Baba and 40 thieves. The boy wanted him to repeat the story of the tiger and bison. When the teacher refused, he ran home and the teacher was running after him to catch him. That was what you saw the other day. But the teacher, being afraid, told you he was trying to keep up the boy’s spirit. The boy is not learning anything except to make mischief and trouble the poor teacher. Question 20. The teacher – student relationship in Crime and Punishment is entirely different from the present day teacher-student relationship. Write your experience/ relationship, with one of your teachers to be published on Teacher’s Day in My Experience page of a Daily. Answer: Carmel is my best teacher. She loves me like her son. Being a nun, she has no child of her own, but she knows how to love children. She is my Class Teacher iri,Glass XII. She encourages me to work hard and achieve success in life. I am a bit weak in my English. She gives me special homework and corrects it and explains to me things very clearly. She taught me in Class XI also. In these two years of her teaching she has never scolded me. She teaches with a smile. She has a nice voice and students can hear her distinctly. She is a good disciplinarian, but she is not harsh to anyone. She reasons with the law-breakers and tells them the importance of discipline in life. She taught me to have strong faith in God. She very clearly told me faith alone would not bring marks in the examinations! We should work hard first and then we must pray God to help us. Well, I believe I have been following her advice. What is interesting about her class is that she tells so many interesting stories to keep the class lively. These stories have real value in the life of the students. She taught me Robert Frost, the American poet. In his poem “Stopping by Woods on a Snowy Evening,” Frost wrote: The woods are lovely, dark and deep, But I have promises to keep, And miles to go before I sleep, And miles to go before I sleep. Sr. Carmel explained to me the deeper meaning of the poem. Yes, I too have promises to keep and miles to go before I sleep. I remember Sr. Carmel everyday and I pray for her health and long life. Think And Write Question 1. Do you think the boy made the mistake purposefully? Why? Answer: I do think the boy made the mistake purposefully. He wanted to annoy the teacher and thus force him to stop teaching him. He wanted to stop learning and start playing. Question 2. How do the parents try to bring up their child as a healthy citizen? Answer: The parents try to bring up their child as a healthy citizen by letting no prohibition or repression affect the boy’s mind. They thought that if they made restrictions and repressions, they would damage him for life. It will need a lot of discipline on the part of the parents. But it is worth it. Question 3. How does the boy blackmail the teacher throughout die story? Answer: The boy blackmails the teacher throughout the story by telling him that he would tell his parents that he had slapped him on his cheek. There was the red mark on his cheek as the proof. Question 4. Why does the teacher support the boy at the end of die story? Answer: The teacher supports the boy at the end of the story because through looks and gestures he appealed to the teacher not to betray him. Question 5. Do you think the story is a satire on over-parenting? Answer: Yes, I do think the story is a satire on over-parenting. They have only one child and they think no prohibitions or repressions should affect his mind’. They built him a nursery, bought him expensive toys, fitted up miniature furniture sets, gave him a small pedal motor car to move about in the garden. His cupboard was filled with chocolates and biscuits which he could eat as he wanted. Question 6. Do you think the mischievous nature of the child is the result of his loneliness? Why? (Mark 2) Answer: I certainly think the mischievous nature of the child is the result of his loneliness. He does not have any peers to play with or exchange ideas with. He is either with the teacher or with his parents, who all are grown-ups. Question 7. Justify the title or the story. Can you suggest a new one? (Mark 2) Answer: The title is short, sweet and apt. Still I think the word ‘crime’ is a bit too harsh. After all, the boy is doing only some small mischievous acts natural to kids. A title I would suggest is: Spare the Rod, Spoil the Child. Question 8. Bring out the humour in the story. (Mark 3) Answer: The story “Crime and Punishment” is very humorous. The title itself is funny to me because when I saw it first I was reminded of the novel of the same name by the world famous Russian writer Fyodor Dostoyevsky. Here the crime consists of simple antics by a prankster. There is humour when the parents talk of the boy as a wingless angel, with dimples, smiles and sweetness. The most humorous part is when the teacher is acting like a stationmaster and when he is running after the boy in the garden to catch him. Activity – I (Indirect speech into direct speech) Look at this paragraph from the story: His parents said that the boy was a little angel, all dimples, smiles and sweetness – only wings lacking. He was their only child, they had abundant affection and ample money. In the above paragraph, the words spoken by the parents are merely reported (Reported speech). Question 1. Write in direct speech. Answer: His parents said: “Our boy is a little angel, all dimples, smiles and sweetness – only wings lacking. He is our only child. We have abundant affection and ample money.” Now discuss in groups, the differences that you notice between direct and indirect speech, and write down your findings. a) The boy – our boy b) Past tense – present tense c) Their – our d) They – we e) The word that is left out in direct speech 0 Change in the punctuations – use of colon and inverted commas. Question 2. Rewrite the following sentences into indirect speech. Answer: The boy immediately switched on to another demand. He said to the teacher: “Tell me a story.” The teacher: “You have not done a sum and it is 8.30.” The boy: “I don’t care for sums. Tell me a story.” The teacher: “No.” The boy: “Appa, Appa!” The teacher: Why are you shouting like that for your father?” The boy: ‘I have something to tell him, something important.” Activity – II (Prepositions) Question 1. Read the sentences from the story and the notes on prepositions given on p. 156. Now, insert suitable prepositions in the following blanks: Answer: a. “You must never set up any sort of contrariness or repression in the child’s mind”, declared the parents. “You’ll damage him for life. It no doubt requires a lot of discipline on our part, but it is worth it”, they declared primly. “We shall be bringing ug a healthy citizen.” b. The teacher was obliged to begin the story of a bison and a tiger, and the he passed on to ‘Ali Baba and the Forty Thieves’ and ‘Aladdin’s Lamp’. The boy listened, rapt and ordered: “I want to hear the story ofthe bison again. It is good…” The teacher was short of breath. He had done six hours of teaching at school during the day. A combination of two independent linguistic units, a preposition and a complement is called a prepositional phrase. Read the examples and notes give on p. 156 & 157. Question 2. Now read the following sentences and find out the prepositional phrases and identify what type of complementation they involve. Also, identify the structures where complements are not used. Answer: a. In one hour b. In private c. Went out – no complement d. Ran off – no complement a. 1. I will come back in one hour. 2. You can do a lot of work in one hour. b. 1. I would like to talk to you in private. 2. We should not disclose things we talked in private. c. 1. After posting the letter he went out. 2. She finished her work and she went out. d. 1. After the accident, the driver ran off. b. After committing the theft, the thief ran off. Activity – III (Using ‘as if’) Read the sentences a & b on p.157. Question 1. Do you think that the underlined words are incorrectly structured? Answer: No, they are not. They are correctly structured. (Read the explanation given there.) Question 2. Now write as many sentences as possible using such a structure. Answer: (Three are already in the text) 1. He behaved as if he were the Principal of the college. 2. He was batting as if he were Sachin Tendulkar. 3. She was speaking as if she were Aishwarya Rai. 4. The politician was behaving as if he were a pauper. 5. Joe was talking as if he were the richest boy in the campus. 6. He was dancing as if he were Michael Jackson. 7. The boy was fighting as if he were Bruce Lee. Activity – IV (Essay writing) Question 1. “Spare the rod and spoil the child was a dictum prevalent in the past What is your opinion about it? Should there be any type of corporal punishment in a learning environment? If so, what should be the mode? Discuss the topic in groups and prepare an essay. Answer: The children nowadays are too difficult to educate. They don’t have much respect for their parents or for other adults. For this reason, parents don’t know what to do with their children and they become desperate. Because of this desperation, they can’t find other ways than beating their children to make them leam and disciplined. I feel this can be useful in some cases if done in a controlled manner. But if you use the rod in excess, it can cause serious problems for the child and also for the family. So the question comes, “Is it really necessary to beat children to educate them?” Many people think that if you educate a small child using the rod, beating him and punishing him, you can have a good control over him. They feel that they can somehow know that the child will behave well and that he will leam to have respect for his parents and others. They feel it would be easier to teach the child good manners by using the rod. But rough treatment makes the child also behave in a cruel mannerto others as he thinks cruelty is an approved form of punishing somebody who does not do as you wish. On the other handfish treatment makes him tough. This toughness can be very useful in future because he is sure to face difficulties and problems in life. A child brought up in a loving manner, in comfort and luxury, will feel puzzled when he is faced with realities outside his home. Punishment has its negative sides. It kills the initiative and curiosity in children. It makes them less adventurous. They will grow into shy and withdrawn persons and they won’t be respected by others. They will lose confidence and they will be always worried if their actions will be approved by others. Scholars and even psychologists differ in their views regarding using the rod on children. The fact is it is a highly controversial issue and there is no definite answer to the question “Should the rod be spared?” I remember a story. A criminal was about to be hanged and the judge asked him what his last wish was. He said he wanted to see his mother. She was brought. The criminal embraced the mother, and as he was embracing her he bit off the tip of her nose. All were appalled at this heinous act. He explained: If this woman had used the rod when I did small mistakes, I wouldn’t have grown into a criminal and reached this stage! I want this to be a warning to parents who give their children freedom to do what they want!” I am sure he had a point. Activity – V: Spelling Read the 3 sentences on page 158. There are some words in them with ‘ie’and ‘ei’ combinations (thieves, relieved, mischievously). (Mark 3) Find more words with re and ‘ei’ combinations: Answer: ‘ie’ words: ‘ei’ words”: ceiling receipt receive deceive conceive perceive conceit deceit The rule to be followed is: i before e except after c. Activity – VI (Let’s edit) Question 1. The following letter contains some prepositions that have been used incorrectly. Identify the errors and edit the letter. Answer: To: Mehas Mehta June 6,2015 Sub: Recommendations for smart phone purchase. Last week, Marisol asked me to provide you with a comparison of the top ‘smart’ phones. He explained that Ad Tech might purchase smart phones for all 25 sales representatives and service technicians. I have studied product capabilities and published reviews of the three smart phones that received the highest rating of PC World Magazine: Palm Treo 600, T-Mobile Sidekick and Blackberry 7210. All the three provide high quality phone service. They key criteria for selection are ease for use and the ability to meet potential needs created by possible expansion of our business. I shall send the recommendations to you, to youre-mail. With regards, Kenneth Abvey Activity – VII (Script writing) Question 1. Your class has decided to stage a play during the School Day celebrations. Prepare a script for the play based on the story‘Crime and Punishment”. (Mark 8) Read the sample script given on page 159. Answer: CRIME AND PUNISHMENT (It is late afternoon. A nursery near a school.) (A TEACHER, looking tired, but stem, is standing. He has a small book in his hand. A STUDENT, quite mischievous looking, is toying with his pen. He is looking at something outside.) Teacher: What is sixteen and three multiplied? (The student just blinks.) Answer me! What is sixteen and three multiplied? Student: (Promptly) Twenty-four. (He has a wicked smile on his lips.) Teacher: (Angrily) How much? Student: I said twenty-four. (Teacher slaps the boy hard on the cheek. The boy looks at him and bursts into tears. Teacher is appalled.) Teacher: Dont’ cry, little boy! You mustn’t Student: I will tell them. Teacher: No, no, no, please don’t. Student: I’ll tell my mother. Teacher: You mustn’t cry for these trifling matters. You must be like a soldier! Student: A soldier? A soldier will shoot with a gun if he is hit. (The teacher laughs taking it as a joke. The student also laughs.) Teacher: Go and wash your face. Student: I’ll wash my face if you close the lessons today. Teacher: No. I can’t do that. Student: Then I will go and tell my mother. (The student tries to get up and go. The teacher forces him to sit down.) Teacher: My dear fellow, I’m to be here for another hour. Student: Alright. Watch me put the engine on its rails. Teacher: If your father comes in …. Student: Tell him it is an engine lesson. (He goes to his cub-board, opens it, takes out his train set and starts assembling the track. He winds the engine and puts it down and it moves round and round.) (To the teacher) You are the station master. Teacher: No, no. You have yourteststhe day aftertomorrow.” Student: (With a wicked smile) Will you be a station master or not? Teacher: (Angrily) I won’t be a station master. Student: Oh, oh, is that what you day? (He gently touches his cheek.) It’s paining me here awfully. I must see my mother. (He moves towards the door.) Teacher: Don’t boy. You want me to be a station master? What shall I have to do? Student: When the train comes to your station, you must blow the whistle and shout, “Engine Driver, stop the train! There are a lot of people who have bought tickets.” (The TEACHER sits in a corner. The STUDENT continues playing. After 30 minutes the teacher gets bored and the boy is unhappy. Fortunately for the TEACHER, the train suddenly refuses to move. The boy picks it up and gives it to the teacher.) Repair it, sir. Teacher: I can’t. I know nothing about it. Student: It must go. Teacher: (Tries to do something to it. But does not succeed. The boy stamps his foot angrily, waiting like a tyrant.) I can’t and I won’t. Student: Okay then. Tell me a story. Teacher: Story? You haven’t done the sum. It is already 8.30. Student: I don’t care for sums. Tell me a story. Teacher: Appa! Appa! Teacher: Why are you shouting like that for your father? Student: I have something to tell him, something important… Teacher: Okay, okay. I will tell you stories. The teacher told the stories of A bison and a Tiger, Ali Baba and 40 Thieves and Aladdin’s Lamp. Student: I want to hearthe story of the bison again. It isgood … Teacher: I’m tired, boy. I’ll tell you tomorrow. I’ve lost all my breath. Student: Oh! Alright. I’ll go and tell… (He runs towards the house, the teacher after him. The teacher is soon tired and sits on the portico step. The parents come out of the house. Father: (To the teacher) What’s the matter? (To the boy) Why have you been running in the garden at this hour? Teacher: (Tired of the boy’s blackmailing) I will explain Father: How’s he preparing for his test in arithmetic? (Hearing the word ‘test’ by the boy is sad. He hides behinds his parents and gestures to the teacher not to betray him. The teacher feels sorry for him.) Teacher: Only please let him mug up the 16th table a little more. He is alright. He will pull through. Good night, Sir; we finished our lessons early, and I was just playing about with the child … something to keep up his spirits, you know! Crime and Punishment (Short story) About The Author R.K. Narayan (1906-2001) is a famous Indian writer in English. He was born in Chennai and educated at Mysore. His novels and stories are set in the imaginary town of Malgudi. His stories are noted for their irony, humour, romance, energy of life and freshness of themes from everyday life. He writes with simplicity. He has written many books. One of his famous books ‘The Guide’ was made into a famous movie with Dev Anand and Wahida Rahman in the lead roles. It ran to full houses for months. #### Crime and Punishment (Short story) Summary in English Page 150: The teacher asked the boy to tell the result of 16 multiplied by 3. The boy blinked. The teacher repeated the question. The boy promptly answered ’24’. The teacher felt that there was a wicked smile on the lips of the boy when he gave the answer. The boy, he felt, was trying to fool him. He had corrected this mistake many times. Then why is the boy persisting in saying 24? How could this fellow get 50 in the class test? The boy’s parents wanted him to have a double promotion and go to the first Form. To get double promotion he should get 50 in the class test. The teacher felt very angry with the boy for giving the wrong answer. He repeated the question, as a last chance. The boy repeated the same answer. The teacher slapped the boy on the cheek. The boy looked at the teacher and burst into tears. The teacher was surprised by his own action and asked the boy not to cry. But the boy said he would tell his parents. The teacher appealed to him not to inform his parents. He was worried. Fortunately this nursery was a little away from the main building. The boy said that he would tell his mother. His parents had once said that the boy was a small angel all dimples, smiles and sweetness. He lacked only the wings. He was their only child. Page 151: They had a lot of love and also money. They built a nursery, bought him expensive toys, fitted up miniature furniture sets, gave him a small pedal motor car to move about in the garden. His cupboard was filled with chocolates and biscuits which he could – eat as he wanted. The parents thought that no prohibition or repression – should affect the boy’s mind. If you make restrictions and repressions, you will damage him for life. It will need a lot of discipline on the part of the parents. But it is worth it. They wanted to bring up a healthy citizen. The teacher agreed outwardly. He felt more and more convinced that what the boy needs was not cajoling but beating. The teacher had a very hard life. The only relief for him was the 30 rupees they paid him every month. It took him 3 hours every evening. The first 72 hour he had to listen to the parents who would talk to him on child psychology. The father had written a thesis on infant psychology for his M.A. The mother had studied a good deal of it for her B.A. Both of them lectured to the teacher. It seemed they wanted him to treat the boy as if he was made of thin glass. The teacher had to agree with them although he knew he was managing a little gorilla. The teacher did not know how to quieten the boy who was still sobbing. He told the boy that he should not cry for small things, but should behave like a soldier. The boy said that a soldier would shoot with a gun if he was hit. The teacher took it as a joke and laughed. The boy also laughed. The teacher then asked the boy to go and wash his face. There was a fine blue porcelain closet attached to the nursery. The boy disobeyed and commanded the teacher to close the lessons for the day. The teacher said no. Page 152: The boy then threatened to tell his mother. He got up from the chair. The teacher held him down saying that he was to be there for another hour. Then the boy said that he should watch him put the engine on its rails. The teacher was worried if the boy’s father came in there would be problems. The boy gave a suggestion: the teacher should say it is an engine lesson. He then went to the cupboard and took out a train set. He started assembling the track. He wound the engine and put it on the track and it went round and round. He wanted the teacher to be the station master. The teacher refused telling him that the boy had his tests after two days. The boy again asked him to be a station master. The teacher got angry. He said he did not want to be a station master. The boy touched his cheek and said it was still paining him and he wanted to see his mother. He moved towards the door. The boy’s cheek was still red. So the teacher asked what he should do as a station master. The boy told him that when the train reached his station he must blow the whistle and ask the train driver to stop the train as there are many people who have bought tickets. The teacher obeyed. He grew tired of the game in 30 minutes. He got up. The boy was unhappy. Luckily for the teacher, the train refused to move. The boy handed it to the teacher and told him to repair it. The teacher turned it around in his hand and said he did not know anything about it. The boy insisted that the train must go. The teacher did not know what to do as he was not a mechanical minded man. He did not know even to turn a screw even it was to save his life. The boy stamped his foot and was waiting like a tyrant. The teacher put it away saying he could not do it. The boy then wanted the teacher to tell him a story. The teacher told the boy that it was 8.30 and he still had not done the sum. Page 153 : The boy insisted on hearing a story. When the teacher said no, he boy started calling his father. When the teacher asked him why he was calling his father, he said he had something important to tell him. The teacher began the story of a bison and a tiger. Then he moved on to Ali Baba and the 40 Thieves. Then he proceeded to Aladdin’s Lamp. The boy was listening intently. He said he wanted to hear the story of the bison again. The teacher was out of breath. He had done 6 hours of teaching at school during the day. He told the boy that he would say that story the next day as he had lost all his breath. The boy then threatens to tell his parents about the slapping. He starts running towards the house, the teacher following him. The boy was too fast for him and made the teacher run round the garden three times. The teacher looked beaten. The boy took pity on him and stopped near the rose bush. The moment the teacher reached near him, the boy again ran off. The boy enjoyed the ‘game’ immensely. The teacher was out of breath. He felt a darkness swelling up around him. He sank down on the portico step. At this time the Father and Mother came out of the house. They asked him what happened. The teacher got up, still panting. He could not talk. He had already decided to tell everything and suffer the consequences. He did not want to stand the blackmail by the boy. They asked the boy why he was running round the garden at this time. The boy looked mischievously at the teacher. The teacher was fumbling for words to start his explanation. Suddenly the father asked how the boy was preparing for the test in arithmetic. On hearing the word ‘test’ the boy’s face fell. He went behind his parents and by look and gestures appealed to the teacher not to betray him. The teacher said that the boy was alright; he had only to study the 16th table a bit more. The boy looked relieved. The teacher saw the boy was grateful for his support. He knew he would not tell his parents about the slapping. After wishing the father Good Night, he told him that they had finished the lessons early and they were just playing to keep up the spirits of the boy. #### Crime and Punishment (Short story) Summary in Malayalam #### Crime and Punishment (Story) Glossary ## Plus Two Maths Chapter Wise Questions and Answers Chapter 7 Integrals Students can Download Chapter 7 Integrals Questions and Answers, Plus Two Maths Chapter Wise Questions and Answers helps you to revise the complete Kerala State Syllabus and score more marks in your examinations. ## Kerala Plus Two Maths Chapter Wise Questions and Answers Chapter 7 Integrals ### Plus Two Maths Integrals Three Mark Questions and Answers Question 1. Integrate the following. (3 Score each) 1. ∫sin x sin 2x sin 3 xdx 2. ∫sec2x cos22x dx Answer: 1. We have sinxsin2xsin3x = 1/2 (2sinxsin3x) sin2x = 1/2 (cos2x – cos4x) sin2x = 1/4 (2sin2xcos2x – 2cos4xsi n2x) = 1/4 [sin4x – (sin6x – sin2x)] = 1/4(sin4x + sin2x – sin6x) ∫sin x sin 2x sin 3 xdx = $$\frac{1}{4}$$ ∫(sin 4x + sin 2x – sin 6x)dx = –$$\frac{1}{16}$$ cos4x – $$\frac{1}{8}$$ cos2x + $$\frac{1}{24}$$ cos6x + c. 2. sec2x cos22x = $$\frac{\left(2 \cos ^{2} x-1\right)^{2}}{\cos ^{2} x}$$ = $$\left(\frac{2 \cos ^{2} x}{\cos x}-\frac{1}{\cos x}\right)^{2}$$ = (2cosx – secx)2 = 4cos2x + sec2x – 4 = 2(1 + cos2x) + sec2x – 4 = 2cos2x + sec2x – 2 ∫sec2 x cos2 2x dx = ∫(2 cos 2x + sec2 x – 2)dx = sin 2x + tan x – 2x + c. Question 2. Find $$\int \frac{2+\sin 2 x}{1+\cos 2 x} e^{x} d x$$? Answer: = ∫ex [sec2 x + tan x]dx = ∫ex[tanx + sec2x]dx = ex tanx + c. Question 3. Evaluate $$\int \frac{\sec ^{2} x d x}{\sqrt{\tan ^{2} x+4}}$$? Answer: Put tanx = u, sec2xdx = dy Question 4. Find the following integrals. Answer: (i) I = $$\int_{0}^{\frac{\pi}{2}} \frac{\sin x}{1+\cos ^{2} x} d x$$ Put cosx = t ⇒ -sin xdx = dt When x = 0 ⇒ t = cos0 = 1, (ii) I = $$\int_{0}^{1} x e^{x^{2}} d x$$ Put x2 = t ⇒ 2xdx = dt When x = 0 ⇒ t = 0, x = 1 ⇒ t = 1 I = $$\frac{1}{2} \int_{0}^{1} e^{t} d t$$ = = [e1 – e0] = e – 1. Put sin x = t ⇒ cos xdx = dt When x = 0 ⇒ t = sin0 = 0, (iv) I = $$\int_{0}^{2} x \sqrt{x+2} d x$$ Put x + 2 = t2 ⇒ dx = 2tdt When x = 0 ⇒ t = $$\sqrt{2}$$, x = 2 ⇒ t = 2 (v) I = $$\int_{0}^{\frac{\pi}{2}} \sqrt{\sin x} \cos x d x$$ Put sin x = t ⇒ cos xdx = dt When x = 0 ⇒ t = sin0 = 0, Put tan x = t ⇒ sec2 xdx = dt When x = 0 ⇒ t = tan 0 = 0, Question 5. (i) If f (x) is an odd function, then $$\int_{-a}^{a} f(x)$$ = ? (a) 0 (b) 1 (c) 2$$\int_{0}^{a} f(x)$$ dx (d) 2a Evaluate (ii) $$\int_{-\pi / 2}^{\pi / 2} \sin ^{99} x \cdot \cos ^{100} x d x$$ (iii) $$\int_{-1}^{1} e^{|x|} d x$$ Answer: (i) (a) 0. (ii) Here, f(x) = sin99x.cos100x .then, f(-x) = sin99(- x).cos100(- x) = – sin99 x. cos100 x = -f(x) ∴ odd function ⇒ $$\int_{-\pi / 2}^{\pi / 2} \sin ^{99} x \cdot \cos ^{100} x d x=0$$. (iii) Here, f(x) = e|x|, f(-x) = e|-x| = e|x| = f(x) ∴ even function. we have |x| = x, 0 ≤ x ≤ 1 Question 6. 1. Show that cos2 x is an even function. (1) 2. Evaluate $$\int_{-\pi / 4}^{\pi / 4} \cos ^{2} x d x$$ (2) Answer: 1. Let f(x) = cos2x ⇒ f(-x) = cos2 (-x) = cos2 x = f(x) even. 2. Question 7. Find the following integrals. Answer: Question 8. Find the following integrals. Answer: Add (1) and (2) Question 9. Find the following integrals. 1. $$\int \frac{1}{3+\cos x} d x$$ 2. $$\int \frac{2 x}{x^{2}+3 x+2} d x$$ Answer: 1. $$\int \frac{1}{3+\cos x} d x$$ Put t = tanx/2 ⇒ dt = 1/2 sec2 x/2 dx 2. $$\int \frac{2 x}{x^{2}+3 x+2} d x$$ = $$\int \frac{2 x}{(x+2)(x+1)} d x$$ 2x = A(x + 1) + B (x + 2) when x = -1, -2 = B ; B = -2 when x = -2, -4 = -A ; A = 4 = 4log(x + 2) – 2log (x + 1) + C. ### Plus Two Maths Integrals Four Mark Questions and Answers Question 1. Find the following integrals. Answer: x2 + x +1 = A(x2 + 1) + (Bx + C)(x + 2) Put x = -2 ⇒ 4 – 2 + 1 = 5A ⇒ A = $$\frac{3}{5}$$ Equating the coefficients of x2 ⇒ 1 = A + B ⇒ B = 1 – $$\frac{3}{5}$$ = $$\frac{2}{5}$$ Equating the constants ⇒ 1 = A + 2C ⇒ 2C = 1 – $$\frac{3}{5}$$ = $$\frac{2}{5}$$ ⇒ C = $$\frac{1}{5}$$ ⇒ 1 = A(x – 1) + B(x + 3) Put x = 1 ⇒ 1 = 2A ⇒ A = $$\frac{1}{2}$$ Put x = -3 ⇒ 1 = -4B ⇒ B = – $$\frac{1}{4}$$ Equating the constants; ⇒ 1 = A Equating the coefficients if t; ⇒ 0 = A + B ⇒ B = -1 Question 2. Find the following integrals. 1. ∫ e2x sin3xdx 2. ∫ x sin-1xdx Answer: 1. I = ∫e2x sin3xdx = ∫ sin 3x × e2xdx 2. ∫ x sin-1xdx = ∫ sin-1x × xdx Question 3. (i) Which of the following is the value of $$\int \frac{d x}{\sqrt{a^{2}-x^{2}}}$$? (1) (ii) Evaluate $$\int \frac{2 x}{x^{2}+3 x+2} d x$$ (3) Answer: (i) [sin-1$$\frac{x}{a}$$ + c] (ii) ⇒ 2x = A(x + 1) + B(x + 2) ⇒ Put x = -2 and x = -1, we get A = 4, B = -2 Question 4. 1. Choose the correct answer from the bracket. ∫ex dx = — (e2x + c, e-x + c, e2x + c) (1) 2. Evaluate: ∫ ex sinxdx Answer: 1. ex + c 2. I = ∫ex sinxdx = sinx.ex – ∫cos x.exdx = sin x.ex – (cos x.ex – ∫(- sin x).ex dx) = sinx.ex – cosxex – ∫sinx.exdx = sin x.ex – cos xex – I 2I = sin x.ex – cos xex I = $$\frac{1}{2}$$ex(sinx – cosx) + c. Question 5. (i) f(x)∫g(x) dx – ∫(f'(x)∫g(x) dx)dx (1) (a) ∫f'(x)g{x)dx (b) ∫f(x)g'(x)dx (c) ∫$$\frac{f(x)}{g(x)}$$dx (d) ∫f(x)g(x)dx (ii) Integrate sin-1$$\sqrt{\frac{x}{a+x}}$$dx w.r.to x. (3) Answer: (i) (d) ∫f(x)g(x)dx (ii) ∫sin-1$$\sqrt{\frac{x}{a+x}}$$dx, Put x = a tan2θ, θ = tan-1$$\sqrt{\frac{x}{a}}$$ ⇒ dx = 2a tanθ sec2θ dθ I = ∫sin-1$$\left(\frac{\tan \theta}{\sec \theta}\right)$$ 2a tanθ sec2θ dθ = ∫sin-1(sinθ)2a tanθ sec2θ dθ = 2a∫θ tanθ sec2θ dθ Put tanθ = t, θ = tan-1 t ⇒ sec2θ dθ = dt = 2a ∫ tan-1 t (t) dθ = a[tan2θ.θ – tanθ + θ] + c = a[θ(1 + tan2θ) – tanθ] + c Question 6. Match the following. (4) Answer: Question 7. Evaluate $$\int \frac{x}{\sqrt{x+a}+\sqrt{x+b}} d x$$? Answer: Question 8. Match the following. Answer: 1. 2. ∫sec x(sec x + tan x)dx = ∫(sec2 x + sec x. tan x)dx = tanx + secx + c. 3. ∫e3xdx = $$\frac{e^{3 x}}{3}$$ + c. 4. ∫(sin x + cos x)dx = sin x – cosx + c. Question 9. Consider the integral I = $$\int \frac{x \sin ^{-1} x}{\sqrt{1-x^{2}}} d x$$? 1. What substitution can be given for simplifying the above integral? (1) 2. Express I in terms of the above substitution. (1) 3. Evaluate I. (2) Answer: 1. Substitute sin-1 x = t. 2. We have, sin-1 x = t ⇒ x = sint Differentiating w.r.t. x; we get, $$\frac{1}{\sqrt{1-x^{2}}}$$dx = dt ∴ I = ∫t sin t dt. 3. I = ∫t sin t dt = t.(-cost) -∫(-cost)dt = -t cost + sint + c = -sin-1 x. cos (sin-1 x) + sin(sin-1 x) + c x – sin-1 x.cos(sin-1 x) + c. Question 10. Evaluate $$\int_{0}^{\pi / 4} \log (\tan x) d x$$. Answer: Question 11. Find the following integrals. 1. $$\int \frac{\sec ^{2} x}{\cos e c^{2} x} d x$$ (2) 2. $$\int \frac{1}{x^{2}-6 x+13} d x$$ (2) Answer: 1. $$\int \frac{\sec ^{2} x}{\cos e c^{2} x} d x$$ = $$\int \frac{\sin ^{2} x}{\cos ^{2} x} d x$$ = ∫tan2 xdx = ∫(sec2x – 1)dx = tanx – x + c. 2. $$\int \frac{1}{x^{2}-6 x+13} d x$$ Question 12. Match the following. Justify your answer. Answer: Question 13. (i) ∫sin2x dx = ? (1) (a) 2 cos x + c (b) -2 sin x + c (c) $$\frac{\cos 2 x}{2}$$ + c (d) $$-\frac{\cos 2 x}{2}$$ + c (ii) Evaluate ∫ex sin 2x dx (3) Answer: (i) (d) $$-\frac{\cos 2 x}{2}$$ + c. (ii) Consider I = ∫ex sin 2x dx = ∫sin 2x. exdx = sinx.ex – 2∫cos 2x. exdx = sin 2x.ex – 2 (cos 2x.ex + 2∫sin 2x. exdx) = sin 2x. ex – 2 cos 2x ex – 4 ∫sin 2x. exdx = sin 2x. ex – 2 cos 2x ex – 4I 5 I = sin 2x. ex – 2 cos 2x ex I = $$\frac{e^{x}}{5}$$ (sin 2x – 2 cos 2x). Question 14. 1. Resolve $$\frac{x^{2}+1}{x^{2}-5 x+6}$$ into partial fractions. (2) 2. Hence evaluate ∫$$\frac{x^{2}+1}{x^{2}-5 x+6}$$. (2) Answer: 1. 2. 5x – 5 = A(x – 2) + B(x – 3) x = 2, 5 = -B, B = -5 x = 3, 10 = A, A = 10 (1) ⇒ I = ∫ 1dx + ∫$$\frac{10}{x-3}$$ dx – ∫$$\frac{5}{x-2}$$ dx = x + 10log(x – 3) – 5log(x – 2) + c. Question 15. Evaluate $$\int_{0}^{4}$$ xdx as a limit of sum. Answer: By definition, $$\int_{a}^{b}$$ f(x) dx = (b – a)$$\lim _{n \rightarrow \infty} \frac{1}{n}$${f(a) + f(a + h) +…….+f(a + {n – 1)h)} Here, a = 0, b = 4, f(x) = x, h = $$\frac{4-0}{n}=\frac{4}{n}$$ ⇒ nh = 4 Question 16. 1. Define the real valued function f(x) = |x2 + 2x – 3| (2) 2. Evaluate $$\int_{0}^{2}$$|x2 + 2x – 3|dx. (2) Answer: 1. f(x) = |x2 + 2x – 3| = |(x – 1) (x + 3)| We have; 2. I = $$\int_{0}^{2}$$|x2 + 2x – 3|dx Question 17. Consider the function f(x) = |x|+|x + 1| 1. Define the function f (x) in the interval [-2, 1]. (2) 2. Find the integral $$\int_{-2}^{1}$$ f(x) dx (2) Answer: 1. Given, f(x) = |x|+|x + 1|. We have, Combining these two functions, we get the function f(x). 2. Question 18. Evaluate $$\int_{\sqrt{6}}^{\sqrt{3}} \frac{d x}{1+\sqrt{\tan x}} d x$$. (4) Answer: ### Plus Two Maths Integrals Six Mark Questions and Answers Question 1. (i) Fill in the blanks. (3) (a) ∫ tan xdx = — (b) ∫ cos xdx = — (c) ∫$$\frac{1}{x}$$dx = — (ii) Evaluate ∫sin3 xcos2 xdx (3) Answer: (i) (a) log|secx| + c (b) sinx + c (c) log|x| + c. (ii) ∫sin3 xcos2 xdx = ∫sin2 xcos2 x sin xdx = ∫(1 – cos2 x)cos2 x sin xdx Put cos x = t ⇒ – sin xdx = dt ∴ ∫(1 – cos2 x)cos2 xsin xdx = -∫(1 – t2 )t2dt = ∫(t4 – t2)dt = $$\frac{t^{5}}{5}-\frac{t^{3}}{3}$$ + c = $$\frac{\cos ^{5} x}{5}-\frac{\cos ^{3} x}{3}$$ + c. Question 2. Find the following integrals. Answer: (i) I = ∫(3x – 2)$$\sqrt{x^{2}+x+1} d x$$ Let 3x – 2 = A(2x + 1) + B ⇒ 3 = 2 A ⇒ A = $$\frac{3}{2}$$ ⇒ -2 = A + B ⇒ -2 = $$\frac{3}{2}$$ + B ⇒ B = -2 – $$\frac{3}{2}$$ = – $$\frac{7}{2}$$ Using (2) and (3) in (1) we have; (ii) I = $$\int \frac{2 x-3}{x^{2}+3 x-18} d x$$ Let 2x – 3 = A(2x + 3) + B ⇒ 2 = 2A ⇒ A = 1 ⇒ -3 = 3A + B ⇒ -3 = 3 + B ⇒ B = -6 (iii) I = $$\int \frac{5 x+2}{1+2 x+3 x^{2}} d x$$ Let 5x + 2 = A{6x + 2) + B ⇒ 5 = 6 A ⇒ A = $$\frac{5}{6}$$ ⇒ 2 = 2A + B ⇒ 2 = $$\frac{5}{3}$$ + B ⇒ 2 – $$\frac{5}{3}$$ = $$\frac{1}{3}$$ (iv) I = $$\int \frac{5 x+3}{\sqrt{x^{2}+4 x+10}} d x$$ Let 5x + 3 = A(2x + 4) + B ⇒ 5 = 2A ⇒ A = $$\frac{5}{2}$$ ⇒ 3 = 4A + B ⇒ 3 = 10 + B ⇒ B = -7 Using (2) and (3) in (1) we have; Question 3. Consider the expression $$\frac{1}{x^{3}-1}$$ 1. Split it into partial fraction. (2) 2. Evaluate ∫ $$\frac{1}{x^{3}-1}$$ dx (4) Answer: 1. 1 = A (x2 + x + 1) + (Bx + c)(x + 1), Put x = -1 ⇒ 1 = A(1 + 1 + 1) ⇒ A= $$\frac{1}{3}$$ Equating like terms. 0 = A + B ⇒ B = – $$\frac{1}{3}$$, 1 = A + C ⇒ C = $$\frac{2}{3}$$ 2. Put, x – 2 = D (2x – 1) + E , 1 = 2 D ⇒ D = $$\frac{1}{2}$$, -2 = -D + E ⇒ E = –$$\frac{3}{2}$$ Question 4. (i) Match the following (4) (ii) Consider the function f(x) = $$\frac{x^{4}}{x+1}$$ Evaluate ∫f(x)dx (2) Answer: (i) (ii) Here the numerator is of degree 4 and denominator of degree 1. So to make it a proper fraction we have to divide Nr by Dr. Question 5. 1. Evaluate the as $$\int_{0}^{2}$$x2dx the limit of a sum. (3) 2. Hence evaluate $$\int_{-2}^{2}$$x2dx (1) 3. If $$\int_{0}^{2}$$ f(x)dx = 5 and $$\int_{-2}^{2}$$ f(x)dx = 0, then $$\int_{-2}^{0}$$ f(x)dx = …….. (2) Answer: 1. Here the function is f(x) = x2, a = 0, b = 2 and h = $$\frac{b-a}{n}=\frac{2}{n}$$ $$\int_{0}^{2}$$x2dx = 2. $$\int_{-2}^{2}$$ x2dx = 2 $$\int_{0}^{2}$$x2dx = $$\frac{16}{3}$$ 3. Question 6. Find ∫$$\sqrt{\tan x}$$xdx. Answer: Given; I = ∫$$\sqrt{\tan x}$$xdx, Put tanx = t2 ⇒ sec2xdx = 2tdt ⇒ dx = $$\frac{2 t d t}{1+t^{4}}$$ Question 7. (i) Match the following. (2) (ii) Integrate $$\frac{\sec ^{2} x}{5 \tan ^{2} x-12 \tan x+14}$$ w.r.to x. (4) Answer: (i) Question 8. 1. Evaluate $$\int_{0}^{1} \sqrt{x} d x$$ (1) 2. If $$\int_{0}^{a} \sqrt{x} d x=2 a \int_{0}^{\pi / 2} \sin ^{3} x d x$$, find the value of a. (3) 3. Hence find $$\int_{a}^{a+1}$$x dx. (2) Answer: 1. 2. Given; 3. When a = 0 When, a = 4 Question 9. (i) Let f (x) be a function, then $$\int_{0}^{a}$$ f(x) dx = ? (1) (a) 2 $$\int_{0}^{a}$$ f(x – a) dx (b) $$\int_{0}^{a}$$ f(a – x) dx (c) f(a) (d) 2$$\int_{0}^{a}$$ f(a – x) dx Evaluate Answer: (i) (b) $$\int_{0}^{a}$$ f(a – x) dx (ii) (1) + (2) ⇒ I = 1. (iii) Question 10. Find the following integrals. 1. ∫$$\frac{2 e^{x}}{e^{3 x}-6 e^{2 x}+11 e^{x}-6} d x$$ 2. ∫$$\frac{(3 \sin x-2) \cos x}{5-\cos ^{2} x-4 \sin x} d x$$ Answer: 1. ⇒ 1 = A(t – 2)(t – 3) + B(t – 1)(t – 3) + C(t – 1)(t – 2) Put t = 1 ⇒ 1 = A(-1)(-2) ⇒ A = $$\frac{1}{2}$$ Put t = 2 ⇒ 1 = B(1)(-1) ⇒ B = -1 Put t = 3 ⇒ 1 = B(2)(1) ⇒ B = $$\frac{1}{2}$$ 2. I = ∫$$\frac{(3 \sin x-2) \cos x}{5-\cos ^{2} x-4 \sin x} d x$$dx Put sin x = t ⇒ cosxdx = dt ⇒ 3t – 2 = A(t – 2) + B Equating the coefficients if t; ⇒ 3 = A Equating the constants ⇒ -2 = -2A + B ⇒ -2 = -6 + B ⇒ B = 4 Question 11. 1. Find ∫$$\frac{1}{x^{2}+a^{2}}$$dx (1) 2. Show that 3x + 1 = $$\frac{3}{4}$$(4x – 2) + $$\frac{5}{2}$$ (2) 3. Evaluate $$\int \frac{3 x+1}{2 x^{2}-2 x+3} d x$$ (3) Answer: 1. ∫$$\frac{1}{x^{2}+a^{2}}$$dx = 1/a tan-1 x/a + c. 2. 3x + 1 = A $$\frac{d}{d x}$$(2x2 – 2x + 3) + B = A(4x – 2) + B 3 = 4A; A = 3/4 1 = -2A + B 1 = -3/2 + B, B = 1 + 3/2 = 5/2 ∴ 3x + 1 = 3/4(4x – 2) + 5/2 3. ## Plus Two Computer Science Chapter Wise Questions and Answers Chapter 12 ICT and Society Students can Download Chapter 12 ICT and Society Questions and Answers, Plus Two Computer Science Chapter Wise Questions and Answers helps you to revise the complete Kerala State Syllabus and score more marks in your examinations ## Kerala Plus Two Computer Science Chapter Wise Questions and Answers Chapter 12 ICT and Society ### Plus Two Computer Science ICT and Society One Mark Questions and Answers Question 1. IPR stands for ______. Answer: Intellectual Property Right. Question 2. WIPO stands for _____. Answer: World Intellectual Property Organisation Question 3. ______ is the exclusive rights to prevent unauthorized copying of inventions by a Creator from the Unauthorised person or company. Answer: Patent Question 4. _____ is a unique, simple and memorable sign to promote a brand and hence increase the business and goodwill of a company. Answer: Trademark Question 5. A product or article is designed so beautifully to attract customers. This type of design is called Answer: Industrial Design. Question 6. Aranmula Kannadi, Palakkadan Matta, Marayoor Sarkkara, etc are example of _______. Answer: Geographical indications. Question 7. _____ is the property right that arises automatically when a person creates a new work by his own and by Law it prevents the others from the unauthorized or intentional copying of this without the permission of the creator. Answer: Copyright Question 8. From the following which is the symbol for copyright. (a)$
(c) ®
(d) ™

Question 9.
From the following which is the symbol for Unregistered trademark.
(a) $(b) © (c) ® (d) ™ Answer: (d) ™ Question 10. From the following which is the symbol for Registered trademark. (a)$
(c) ®
(d) ™
(c) ®

Question 11.
Unauthorized copying or use of Intellectual property rights such as Patents, Copyrights and Trademarks are called ____.
Intellectual Property Infringement.

Question 12.
_____ prevents others from the unauthorized or intentional copying or use of Patent without the permission of the creator.
Patent Infringement.

Question 13.
______ is the illegal copying, distribution, or use of software.
Piracy.

Question 14.
______ prevents others from the unauthorized or intentional copying or use of Trademark without the permission of the creator.

Question 15.
_____ prevents others from the unauthorized or intentional copying or use of Copy right without the permission of the creator.
Copy right Infringement

Question 16.
______ is a virtual environment created by computer systems connected to the internet
Cyberspace

Question 17.
A person committing crimes and illegal activities with the use of computers over Internet. This crime is included as _____ crime.
Cybercrime

Question 18.
State True or False.
Cybercrimes can be classified into three categories such as against individual, property, and Government.
True

Question 19.
Phishing, hacking, denial of service attacks, etc are ____ crimes.
Cyber

Question 20.
Odd one out
(а) Identity theft
(b) Harassment
(c) violation of privacy
(d) credit card fraud
(d) credit card fraud, it is a cybercrime against individual others are cyber crimes against property.

Question 21.
Odd one out
(a) Credit card theft
(b) Intellectual property theft
(c) Internet time theft
(d) Dissemination of obscene material
(d) Dissemination of obscene material, It is cyber , crime against individual, the others are cyber against property.

Question 22.
Odd one out
(a) cyberterrorism
(b) Attacks against e-Governance websites
(c) Impersonation and cheating
(d) Website defacement
(c) Impersonation and cheating, it is cybercrime against individual others are cyber crimes against Government.

Question 23.
IT Act amended in _____.
(a) 2015
(b) 2008
(c) 1900
(d) 1998
(b) 2008

Question 24.
IT Act passed in Indian parliament is ____.
2000.

Question 25.
The laws to prevent cyber crimes is termed as ____.
Cyberlaw

Question 26.
_____ excessive enthusiasm for acquiring knowledge.
Infomania

Question 27.
Phishing is an example of ______.
Cybercrime.

Question 28.
ICT stands for _______.
(a) Internet and Communication Technology
(b) Information and Computer Technology
(c) Information and Communication Technology
(d) Integrated Communication Technology
(c) Information and Communication Technology

Question 29.
Which of the following e-Governance helps citizens for interacting with the Government?
(a) G2E
(b) G2B
(c) G2C
(d) G2G
(c) G2C

Question 30.
What are the different types of interactions in e-Governance?
G2G, G2E.G2B, G2C.

Question 31.
The unauthorized use of intellectual property rights is termed as
Infringement

Question 32.
Expand the term WIPO in connection with IPR.
World Intellectual Property Organization.

Question 33.
The exclusive right granted to an invention is called
(b) Copy right
(c) Patent
(d) Design
(c) Patent

Question 34.
The exclusive right given to a person over the creation of his/her mind for a period of time is called
Patent / Intellectual Property Right

Question 35.
What is the name given to the process of using scientific knowledge for analyzing and presenting evidence of cyber related crimes before court?
Cyber forensics

Question 36.
Which among the following are considered as violation to privacy?
1. Keeping hidden cameras in private places
2. Publishing private photos of individual in social media without their permission
3. Use of unauthorized software
(A) All the above are correct
(B) 1,2 and 3 only
(C) 1 and 4 only
(D) 1 and 2
(D) 1 and 2

### Plus Two Computer Science ICT and Society Two Mark Questions and Answers

Question 1.
“IPR (Intellectual Property Right) encourages innovation” Justify.
Some people spend lots of money,time body and mental power to create some products such as a classical movie, album, artistic work, discoveries, invention, software, etc. These type of Intellectual properties must be protected from unauthorized access by law. This is called Intellectual Property right(IPR). It enables to earn recognition, financial benefit, can sell the innovation, etc. It motivates further innovation.

Question 2.
Define the following terms.

1. Cyber space
2. Cyber crime

1. CyberSpace:
Earlier Traditional communication services such as postal service(Snail mail) are used for communication. It is a low speed and not reliable service. In order to increase the speed Telegram Services were used. Its speed was high but it has lot of limitations and expensive too.

Later telephones were used for voice communication. Nowadays telephone system and computer system are integrated and create a virtual(un real) environment. This is called cyber space. The result for this integration is that tremendous speed and it is very cheap.

2. Cyber crime:
Just like normal crimes (theft, trespassing private area, destroy, etc,) Cyber crimes (Virus, Trojan Horse, Phishing, Denial of Service, Pornography, etc) also increased significantly. Due to cyber crime, the victims lose money, reputation, etc and some of them commit suicide.

Question 3.
Write a short note on

2. Industrial design

This is a unique, simple and memorable sign to promote a brand and hence increase the business and goodwill of a company. It must be registered. The period of registration is for 10 years and can be renewed. The registered trademark under Controller General of Patents Design and Trademarks cannot use or copy by anybody else.

2. Industrial designs:
A product or article is designed so beautifully to attract the customers. This type of designs is called industrial design. This is a prototype and used as a model for large scale production.

Question 4.
1. Patents:
A person or organization invented a product or a creation can be protected from unauthorized copying or creation without the permission of the creator by law. This right is called Patent. In India the validity of the right is up to 20 years. After this anybody can use freely.

This is a unique, simple and memorable sign to promote a brand and hence increase the business and goodwill of a company. It must be registered. The period of registration is for 10 years and can be renewed. The registered trademark under Controller General of Patents Design and Trademarks cannot use or copy by anybody else.

Question 5.
Write any one website for the following services.

1. e-Governance
3. e-Banking
4. e-Learning

1. e-Governance(any One) www.dhsekerala.gov.in, www.incometaxindia.gov.in, www.spark.gov.in,www.ceo.kerala.gov. in
3. e-Banking www.onlinesbi.co.in
4. e-Learning www.ignouonline.ac.in,www.nptel.iitm.ac.in

Question 6.
Write a short note about EPS.
Electronic Payment System(EPS): It is also called plastic money that is electronically exchange money between two individuals or firms(buyers and sellers) in an online environment.

Question 7.
What is cyberspace?
Earlier Traditional communication services such as postal service(Snail mail) are used for communication. It is a low speed and not reliable service. In order to increase the speed Telegram Services were used. Its speed was high but it has lot of limitations and expensive too.

Later telephones were used for voice communication. Nowadays telephone system and computer system are integrated and create a virtual(unreal) environment. This is called cyberspace. The result for this integration is that tremendous speed and it is very cheap.

Question 8.
Why is cyberspace called a virtual world?
The telephone system and computer system are integrated and create a virtual(un real) environment. This is called cyber space. The result for this integration is that tremendous speed and it is very cheap. This is an imaginary world. We can see persons with different behaviour. Because of good and bad people we can’t believe blindly. If we search a solution for a problem thousands of answers will get instantly and may confused us.

Question 9.
What is copyright? How does it differ from patent?
The trademark is ©, copyright is the property right that arises automatically when a person creates a new work by his own and by Law it prevents the others from the unauthorized or intentional copying of this without the permission of the creator for 60 years after the death of the author.

2. Patents:
A person or organization invented a product or a creation can be protected from unauthorized copying or creation without the permission of the creator by law. This right is called Patent. In India the validity of the right is up to 20 years. After this anybody can use freely.

Question 10.
Explain the exclusive right given to the owner by IPR?
The exclusive right given to the owner by I PR is owner can disclose their creations for money.

Question 11.
it is the unauthorized copying, distribution, and use of a creation without the permission of the creator. It is against the copyright act and hence the person committed deserve the punishment.

Question 12.
Match the following

a – 2
b – 3
c – 4
d – 1

Question 13.
What do you meant by infringement?
Unauthorized copying or use of Intellectual property rights such as Patents, Copy rights and Trademarks are called intellectual property lnfringement(violation). It is a punishable offence.

### Plus Two Computer Science ICT and Society Three Mark Questions and Answers

Question 1.
Write a short note on the importance of IT Act 2000.
Information Technology Act 2000(amended in 2008):
IT Act 2000 controls the use of Computer(client), Server, Computer Networks, data and Information in Electronic format and provide legal infrastructure for E-commerce, in India. This is developed to promote IT industry, control e-commerce also ensures the smooth functioning of E-Governance and it prevents cyber crimes.

The person those who violate this will be prosecuted. In India, IT bill introduced in the May 2000 Parliament Session and it is known as Information Technology Act 2000. Some exclusions and inclusions are introduced in December 2008.

Question 2.
“Infomania affects peoples’ lives and their loved ones.”
Comment on this statement.
Info mania is excessive desire(infatuation) for acquiring knowledge from various modern sources like Internet, Email, Social media. Instant Message Application(WhatsApp) and Smart Phones. Due to this the person may neglect daily routine such as family, friends, food, sleep, etc. hence they get tired.

They give first preference to Internet than others. They create their own Cyber World and no interaction to the surroundings and the family. They are more anxious and afraid that they will be out from the cyber world unless they updated.

Question 3.

• It overcomes geographical limitations
• It reduces the operational cost
• It minimizes the time and cost
• It remains open all the time
• We can locate the product faster from a wider range of choices
• Peoples are unaware of IT applications and its uses
• Most peoples don’t have plastic money(credit / debit card) and net banking
• It requires high security measurements otherwise you may lose money
• We can’t touch or smell products through online
• Some companies may not have proper Goods delivery service

Question 4.
How do trademark and industrial design differ?
This is a unique, sirhple and memorable sign to promote a brand and hence increase the business and goodwill of a company. It must be registered. The period of registration is for 10 years and can be renewed. The registered trademark under Controller General of Patents Design and Trademarks cannot use or copy by anybody else.

Industrial designs:
A product or article is designed so beautifully to attract the customers. This type of designs is called industrial design. This is a prototype and used as a model for large scale production.

Question 5.
Why is Cyberlaw important?
Just like normal crimes (theft, trespassing private area, destroy, etc.) Cybercrimes (Virus, Trojan Horse, Phishing, Denial of Service, Pornography, etc.) also increased significantly. Due to cybercrime, the victims lose money, reputation, etc. and some of them commit suicide.

Cyberlaw ensures the use of computers and Internet by the people safely and legally. It consists of rules and regulations like Indian Penal Code (IPC) to stop crimes and for the smooth functions of Cyberworld. Two Acts are IT Act 2000 and IT Act Amended in 2008.

Question 6.
“Infomania has became a psychological problem”. Write your opinion.
Info mania is the excessive desire(lnfatuation) for acquiring knowledge from various modern sources like Internet, Email, Social media, Instant Message Application(WhatsApp) and Smart Phones. Due to this the person may neglect daily routine such as family, friends, food, sleep, etc. hence they get tired.

They give first preference to Internet others. They create their own Cyber World and no interaction to the surroundings and the family. They are more anxious and afraid that they will be out from the cyber world unless they updated.

### Plus Two Computer Science ICT and Society Five Mark Questions and Answers

Question 1.
“Due to anonymous nature of Internet it is possible for the people to engage in variety of criminal activities.” Justify the statement with special reference to cyber crimes taking place against individual.
Cyber crimes against individuals
i. Identity theft:
The various information such as personal details(name, Date of Birth, Address, Phone number etc) , Credit / Debit Card details(Card number, PIN, Expiry Date, CW, etc), Bank details, etc. are the identity of a person. Stealing these information by acting as the authorized person without the permission of a person is called Identity theft. The misuse of this information is a punishable offence.

ii. Harassment:
Commenting badly about a particular person’s gender, colour, race, religion, nationality, in Social Media is considered as harassment. This is done with the help of Internet is called Cyber stalking (Nuisance). This is a kind of torturing and it may lead to spoil friend ship, career, self image and confidence. Sometimes may lead to a big tragedy of a whole family or a group of persons.

iii. Impersonation and cheating:
Fake accounts are created in Social Medias and act as the original ICT and Society one for the purpose of cheating or misleading others. Eg: Fake accounts in Social Medias (Facebook, Twitter, etc), fake SMS, fake emails etc.

iv. Violation of privacy:
Trespassing into another person’s life and try to spoil life. It is a punishable offence. Hidden camera is used to capture the video or picture and black mailing them.

v. Dissemination of obscene material: With the help of hidden camera capture unwanted video or picture. Distribute or publish this obscene clips on Internet without the consent of the victims may mislead the people specifically the younger ones.

Question 2.
Explain different categories of cyber crimes in detail.
Just like normal crimes( theft, trespassing private area, destroy, etc,) Cyber crimes(Virus, Trojan Horse, Phishing, Denial of Service, Pornography etc) also increased significantly . Due to cyber crime, the victims lose money, reputation,etc and some of them commit suicide.
A. Cyber crimes against individuals:
1. Identity theft:
The various information such as personal details(name, Date of Birth, Address, Phone number etc.), Credit / Debit Card details(Card number, PIN, Expiry Date, CW, etc), Bank details, etc. are the identity of a person. Stealing these information by acting as the authorized person without the permission of a person is called Identity theft. The misuse of this information is a punishable offence.

2. Harassment:
Commenting badly about a particular person’s gender, colour, race, religion, nationality, in Social Media is considered as harassment. This is done with the help of Internet is called Cyber stalking (Nuisance). This is a kind of torturing and it may lead to spoil friend ship, career, self image and confidence. Sometimes may lead to a big tragedy of a whole family or a group of persons.

3. Impersonation and cheating:
Fake accounts are created in Social Medias and act as the original one for the purpose of cheating or misleading others. Eg: F.ake accounts in Social Medias (Facebook, Twitter,etc), fake sms, fake emails, etc.

4. Violation of privacy:
Trespassing into another person’s life and try to spoil the life. It is a punishable offence. Hidden camera is used to capture the video or picture and black mailing them.

5. Dissemination of obscene material:
With the help of hidden camera capture unwanted video or picture. Distribute or publish this obscene clips on Internet without the consent of the victims may mislead the people specifically the younger ones.

B. Cyber crimes against property:
Stealing credit card details, hacking passwords of social media accounts or mail account or Net banking, uploading latest movies etc, are considered as cyber crimes against property.
1. Credit card fraud:
Stealing the details such as credit card number, company name, expiry date, cw number,password etc. and use these details to make payment for purchasing goods or transfer funds also.

2. Intellectual property theft:
The violation of Intellectual Property Right of Copy right, Trademark, Patent, etc. In film industry crores of investment is needed to create a movie. Intellectual Property thieves upload the movies on the Releasing day itself. Hence the revenue from the theatres are less significantly and undergoes huge loss.(Eg: Premam, Bahubali, etc) Copying a person’s creation and present as a new creation is called plagiarism. This can be identified some tools(programs) available in the Internet

3. Internet time theft:
This is deals with the misuse of WiFi Internet facility. If it is not protected by good password there is a chance of misuse our devices(Modem/Router) to access Internet without our consent by unauthorized persons. Hence our money and volume of data(Package) will lose and we may face the consequences if others make any crimes.

C. Cyber crimes against government:
The cyber crimes against Govt, websites is increased significantly. For example in 2015 the website of Registration Department of Kerala is hacked and destroys data from 2012 onwards.

1. Cyber terrorism:
It is deals with the attacks against very sensitive computer networks like computer controlled atomic energy power plants, air traffic controls, Gas line controls, telecom, Metro rail controls, Satellites, etc. This is a very serious matter and may lead to huge loss (money and life of citizens). So Govt, is very conscious and give tight security mechanism for their services.

2. Website defacement:

3. Attacks against e-governance websites :
Its main target is a Web server. Due to this attack the Web server/ computer forced to restart and this results refusal of service to the genuine users. If we want to access a website first you have to type the web site address in the URL and press Enter key, the browser requests that page from the web server. Dos attacks send huge number of requests to the web server until it collapses due to the load and stops functioning.

Question 3.
“For the implementation of e-Learning different tools.
e Learning tools
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## Plus Two Maths Chapter Wise Questions and Answers Chapter 6 Application of Derivatives

Students can Download Chapter 6 Application of Derivatives Questions and Answers, Plus Two Maths Chapter Wise Questions and Answers helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

## Kerala Plus Two Maths Chapter Wise Questions and Answers Chapter 6 Application of Derivatives

### Plus Two Maths Application of Derivatives Three Mark Questions and Answers

Question 1.
Find the equation of tangents and normals to the given curves x = cost, y = sin t at t = $$\frac{π}{4}$$.
Given; x = cost, y = sin t

Equation of tangent at t = $$\frac{π}{4}$$ is;

Equation of normal at t = $$\frac{π}{4}$$ is;

⇒ $$\sqrt{2}$$y + $$\sqrt{2}$$x = 0 ⇒ y + x = 0.

Question 2.
A ladder Sm long is leaning against a wall. The bottom of the ladder is pulled along the ground, away from the wall, at the rate of 2cm/s. How fast is its height on the decreasing when the foot of the ladder is 4m away from the wall?
From the figure we have;
x2 + y2 = 25 ____(1)

Differentiating w.r.t t;

From (1) when x = 4 ⇒ 16 + y2 = 25 ⇒ y = 3
Given; $$\frac{d x}{d t}$$ = 2cm/s = 0.02 m/s
(2) ⇒ 4(0.02) + 3 $$\frac{d x}{d t}$$ = 0

Question 3.
Find the points on the curve y = x3, the tangents at which are inclined at an angle of 60° to x-axis?
$$\frac{d y}{d x}$$ = 3x2
Slope of the tangent = tan60°
i.e. 3x2 = $$\sqrt{3}$$

Question 4.
Find the equation of the tangent to the parabola y2 = 4x + 5 which is parallel to y = 2x + 7.
y2 = 4x + 5 _____(1)
2y $$\frac{d y}{d x}$$ = 4
$$\frac{d y}{d x}$$ = $$\frac{4}{2y}$$ = $$\frac{2}{y}$$
Given tangent is parallel to y = 2x + 7
ie. Slope of the tangent is 2 ⇒ $$\frac{2}{y}$$ = 2 ⇒ y = 1
∴ from (1) ⇒ 1 = 4x+ 5 ⇒ 4x = -4 ⇒ x = -1
So the point of contact is (-1, 1).
∴ Equation of tangent is
y -1 = 2(x + 1) ⇒ y = 2x + 3.

Question 5.
Find the intervals in which the function f given f(x) = 2x2 – 3x is

1. Strictly increasing.
2. Strictly decreasing.

Given; f(x) = 2x2 – 3x ⇒ f'(x) = 4x – 3
For turning points; f'(x) = 0
⇒ 4x – 3 = 0 ⇒ x = $$\frac{3}{4}$$
The intervals are $$\left(-\infty, \frac{3}{4}\right),\left(\frac{3}{4}, \infty\right)$$
f'(0) = – 3 < 0
∴ Strictly decreasing in $$\left(-\infty, \frac{3}{4}\right)$$
f'(1) = 1 > 0
∴ Strictly increasing in $$\left(\frac{3}{4}, \infty\right)$$.

Question 6.
Find the intervals in which the function f(x) = (x + 1)3 (x – 3)3 strictly increasing or decreasing.
Given; f(x) = (x + 1)3 (x – 3)3
⇒ f'(x) = (x + 1)3 3(x – 3)2 + (x – 3)33(x + 1)2
= 3(x + 1)2(x – 3)2(x + 1 + x – 3)
= 3(x + 1)2(x – 3)2(2x – 2)
= 6(x +1)2 (x – 3)2 (x -1)
⇒ 6(x +1)2 (x – 3)2 (x – 1) = 0
⇒ x = -1, 1, 3
The intervals are
(-∞, -1), (-1, 1), (1, 3), (3, ∞)
f'(-2) = (-2 – 1) < 0
∴ Strictly decreasing in (-∞, -1)
f'(0) = (0 – 1) < 0
∴ Strictly decreasing in (-1, 1)
f'(2) = (2 – 1) > 0
∴ Strictly increasing in (1, 3)
f'(4) = (4 – 1) > 0
∴ Strictly increasing in (3, ∞).

Question 7.
Find the intervals in which the function f(x) = x + $$\frac{1}{x}$$ strictly increasing or decreasing.

⇒ x = ±1
The intervals are (-∞, -1), (-1, 1), (1, ∞)
f'(-2) > 0
∴ Strictly increasing in (-∞, -1)
f'(0) < 0
∴ Strictly decreasing in (-1, 1)
f'(2) > 0
∴ Strictly increasing in (1, ∞).

Question 8.
Determine whether the f(x) = x2 function is strictly monotonic on the indicated interval.

1. (-1, 1)
2. (-1, 0)
3. (0, 1)

f(x) = x2
⇒ f'(x) = 2x
⇒ f'(x) = 0 ⇒ 2x = 0 ⇒ x = 0
This turning point divides the domain into the intervals (-∞, 0); (0, ∞).

1. Interval (-1,1) f'(x) < 0 and f'(x) > 0. So f(x) is not monotonic.
2. Interval (-1,0), f'(x) < 0. ∴ f(x) is strictly monotonic.
3. Interval (0, 1) f'(x) > 0 and f(x) is strictly monotonic.

Question 9.
Determine whether the f(x) = x3 – x function is strictly monotonic on the indicated interval.

1. (-1, 0)
2. (-1, -1/2)
3. (-1, 1)

(x) = x3 -x ⇒ f'(x) = 3x2 – 1
⇒ f'(x) = 0 ⇒ 3x2 – 1 = 0 ⇒ x = ±$$\frac{1}{\sqrt{3}}$$
This turning point divides the domain into the intervals (-∞, $$\frac{1}{\sqrt{3}}$$); (-$$\frac{1}{\sqrt{3}}$$, $$\frac{1}{\sqrt{3}}$$); ($$\frac{1}{\sqrt{3}}$$, ∞).

1. Interval (-1, 0), f'(x) changes sign. So not monotonic.
2. Interval (-1, -1/2), f'(x) > 0 strictly monotonic.
3. lnterval(-1, 1) not monotonic

Question 10.
Find the approximate change in the volume V of a cube of side x meters caused by increasing the side by 1%.
We have; V = x3 and ∆x = 1% of x= 0.01x
dV = $$\frac{d V}{d x}$$ ∆x = 3x2∆x
= 3x2 × 0.01x = 0.03x3 = 0.03V
⇒ $$\frac{d V}{V}$$ = 0.03
Therefore 3% is the approximate increase in volume.

Question 11.
If the radius of a sphere is measured as 7m with an error of 0.02m then find the approximate error in calculating its volume.
Let r be the radius of the sphere and ∆r be the error in measuring the radius then r =7m and ∆r = 0.02 m
We have; V = $$\frac{4}{3}$$ πr3
dV = $$\frac{d V}{dr}$$ ∆r = $$\frac{4}{3}$$ π3r2 × ∆r
= 4π(7)2 × 0.02 = 3.92 π m3.

Question 12.
The length of a rectangle is decreasing at the rate of 5 cm/min and the width is increasing at the rate of 4cm/min. When length is 8 cm and width is 6 cm, find the rate of change of its area.
Let length = x and width = y

Question 13.
Find the equation of tangents and normals to the given curves y= x4 – 6x3 + 13x2 – 10x + 5 at (0, 5)
Given; y = x4 – 6x3 + 13x2 – 10x + 5 at (0, 5)
⇒ $$\frac{d y}{d x}$$ = 4x3 – 18x2 + 26x – 10
Slope = $$\left(\frac{d y}{d x}\right)_{x=0}$$ = -10
Equation of tangent at (0, 5) is;
y – 5 =(-10)(x – 0)
⇒ y – 5 = -10x ⇒ 10x + y – 5 = 0
Equation of normal at (0, 5) is;
y – 5 = $$\frac{1}{10}$$(x – 0)
⇒ 10y – 50 = x ⇒ x – 10y + 50 = 0.

Question 14.
Find the equation of tangents and normals to the given curves y = x3 at (1, 1)
Given; y = x3
⇒ $$\frac{d y}{d x}$$ = 3x2
Slope = $$\left(\frac{d y}{d x}\right)_{x=1}$$ = 3
Equation of tangent at (1, 1) is; y -1 = (3)(x – 1)
⇒ y – 1 = 3x – 3 ⇒ 3x – y – 2 = 0
Equation of normal at (1, 1) is;
y – 1 = $$-\frac{1}{3}$$(x – 1)
⇒ 3y – 3 = -x + 1 ⇒ x+ 3y – 4 = 0.

Question 15.
The volume of a cube is increasing at the rate of 8cm3/s. How fast is the surface area increasing when the length of an edge is 12cm.
Let V be the volume of the cube of side x.
We have volume = V = x3
Rate of change of volume with respect to time ‘t’ is;
ie; differentiating w.r.t t; $$\frac{d V}{d t}$$ = 3x2$$\frac{d x}{d t}$$
Given; $$\frac{d V}{d t}$$ = 8 and x = 12 ⇒ 8 = 3(12)2$$\frac{d x}{d t}$$

Now let Surface area = S = 6x2
Differentiating w.r.t t;

Question 16.
Find the intervals in which the function f(x) = -2x3 – 9x2 – 12x + 1 strictly increasing or decreasing.
Given; f(x) = -2x3 – 9x2 – 12x + 1
⇒ f'(x) = -6x2 – 18x – 12
= – 6(x2 + 3x + 2)
= – 6(x + 2)(x +1)
⇒ f'(x) = 0 ⇒ -6(x + 2)(x +1) = 0
⇒ x = -2, -1
The intervals are (-∞, -2),(- 2, -1),(-1, ∞)
f'(-3) = -(-3 + 2)(-3 + 1) < 0
∴ Strictly decreasing in (-∞, -2)
f'(-1.5) = -(-1.5 + 2)(-1.5 + 1) > 0
∴ Strictly increasing in (- 2, -1)
f'(0) = -(0 + 2)(0 + 1) < 0
Strictly decreasing 1n(-1, ∞).

Question 17.
Find the local maxima and minima of the following functions. Also find the local maximum and minimum values. (each question carry 3 score)

1. f(x) = sin x + cosx, 0 < x < $$\frac{\pi}{2}$$
2. f(x) = x3 – 3x
3. f(x) = x3 – 6x2 + 9x + 15
4. g(x) = $$\frac{x}{2}$$ + $$\frac{2}{x}$$, x > 0
5. g(x) = $$\frac{1}{x^{2}+2}$$

1. Given; f(x) = sinx + cosx
⇒ f'(x) = cosx – sinx
For turning point f'(x) = 0
⇒ cosx – sinx = 0
⇒ cosx = sinx
⇒ x = $$\frac{\pi}{4}$$
f”(x) = -sin x – cosx
⇒ f ($$\frac{\pi}{4}$$) = -sin$$\frac{\pi}{4}$$ – cos$$\frac{\pi}{4}$$ < 0
Hence f(x) has a local maximum at x = $$\frac{\pi}{4}$$ and local maximum value is

2. Given; f(x) = x3 – 3x
⇒ f'(x) = 3x2 – 3
For turning point f'(x) = 0
⇒ 3x2 – 3 = 0
⇒ x = ±1
f”(x) = 6x
When x = -1
⇒ f”(-1) = -6 < 0
Hence f(x) has a local maximum at x = -1 and local maximum value is
f(-1) = (-1)3 – 3(-1) = -1 + 3 = 2
When x = 1
⇒ f”(1) = 6 > 0
Hence f(x) has a local minimum at x = 1 and local minimum value is
f(1) = (1)3 – 3(1) = 1 – 3 = -2.

3. Given; f(x) = x3 – 6x2 + 9x + 15
⇒ f'(x) = 3x2 – 12x + 9
For turning point f'(x) = 0
⇒ 3x2 – 12x + 9 = 0 ⇒ 3(x2 – 4x + 3) = 0
⇒ 3(x – 1)(x – 3) = 0 ⇒ x = 1, 3
f”(x) = 6x – 12
When x = 1
⇒ f”( 1) = 6 – 12 < 0
Hence f(x) has a local maximum at x = 1 and local maximum value is
f(1) = (1)3 – 6(1)2 + 9(1) + 15 = 19
When x = 3
⇒ f”(3) = 6(3) – 12 > 0
Hence f(x) has a local minimum at x = 3 and local minimum value is
f(3) = (3)3 – 6(3)2 + 9(3) + 15 = 15.

4. Given; g(x) = $$\frac{x}{2}$$ + $$\frac{2}{x}$$
⇒ g'(x) = $$\frac{1}{2}$$ – $$\frac{2}{x^{2}}$$
For turning point g'(x) = 0

Since x > 0, the acceptable value of x = 2

Hence g(x) has a local maximum at x = 2 and local maximum value is g(2) = $$\frac{2}{2}$$ + $$\frac{2}{2}$$ = 2

5. Given; g(x) = $$\frac{1}{x^{2}+2}$$

For turning point g'(x) = 0

Hence g(x) has a local maximum at x = 2 and maximum value is g(2) = $$\frac{1}{0+2}=\frac{1}{2}$$.

Question 18.
Find the absolute maximum value and minimum value of the following functions.

1. f(x) = x3, x ∈ [-2, 2]
2. f(x) = 4x – $$\frac{x^{2}}{2}$$, x ∈ $$\left[-2, \frac{9}{2}\right]$$

1. Given; f(x) = x3 ⇒ f'(x) = 3x2
For turning point f'(x) = 0 ⇒ 3x2 = 0 ⇒ x = 0
f(- 2) = (-2 )3 = -8
f( 2) = (2)3 = 8
f(0) = (0)3 = 0
Absolute maximum = max{-8, 8, 0} = 8
Absolute minimum = min {-8, 8, 0} = – 8

2. Given; f(x) = 4x – $$\frac{x^{2}}{2}$$ ⇒ f'(x) = 4 – x
For turning point f'(x) = 0 ⇒ 4 – x = 0
⇒ x = 4

Absolute maximum = max{-10, 8, 7.875} = 8
Absolute minimum = min {-10, 8, 7.87} = -10.

Question 19.
A television camera at ground level is filming the lift-off of a space shuttle that is rising vertically according to position equation S = 50t2.
The camera is 2000 feet from the launch pad. Find the rate of change in the angle of elevation of the camera 10 seconds after lift-off.

Question 20.
Determine whether the f(x) = sinx function is strictly monotonic on the indicated interval.

1. (0, 2π)
2. (0, π)
3. (-π/2, π/2)

f(x) = sinx ⇒ f'(x) = cosx changes sign.

1. Interval (0, 2π). ∴ f(x) is not monotonic.
3. f'(x) > 0 in (-π/2, π/2), ie. f(x) is strictly monotonic.

Question 21.
Find the approximate change in the Surface Area of a cube of side x meters caused by decreasing the side by 1%.
We have;
S = 6x2 and ∆x = 1% of x = -0.01x
dS = $$\frac{d S}{d x}$$ ∆x = 6 × 2x × ∆x
= 6 × 2x × -0.01x = -0.02 × 6x2 = -0.02S
⇒ $$\frac{d S}{S}$$ = -0.02
Therefore 2% is the approximate decrease in surface area.

### Plus Two Maths Application of Derivatives Four Mark Questions and Answers

Question 1.
The length ‘x’ of a rectangle is decreasing at the rate of 2 cm/s and the width ‘y’ is increasing at the rate of 2 cm/s.

1. Find the rate of change of Perimeter.
2. Find $$\frac{d A}{dt}$$ when x = 12 cm and y = 5 cm.

Since the length ‘x’ is decreasing and the width ‘y’ is increasing, we have $$\frac{d x}{dt}$$ = -2 cm/s and $$\frac{d y}{dt}$$
= 2 cm/sec.
1. The Perimeter ‘P’ of the rectangle is given by
P = 2 (x + y)

2. The area ‘A’ of the rectangle ‘A’ is given by
A = x.y

= 12(2) + 5(-2)
= 24 – 10 = 14 cm2/s.

Question 2.
Find the equation of all lines having slope -1. Which are tangents to the curve?
y = $$\frac{1}{x-1}$$, x ≠ 1

⇒ x2 – 2x = 0 ⇒ x(x – 2) = 0 ⇒ x = 0, x = 2
At x = 0, y = -1
Equation of tangent at (0, -1) is;
At x = 2, y = $$\frac{1}{2-1}$$ = 1
Equation of tangent at (2, 1) is; y – 1 = -1(x – 2)
⇒ y – 1 = -x + 2 ⇒ x + y – 3 = 0.

Question 3.
Find the points on the curve x2 + y2 – 2x – 3 = 0 at which the tangent are parallel to x-axis.
Given; x2 + y2 – 2x – 3 = 0
Differentiating with respect to x;

Since the tangent is parallel to x-axis $$\frac{d y}{d x}$$ = 0
$$\frac{1-x}{y}$$ = 0 ⇒ x = 1
We have; (1)2 + y2 – 2(1) – 3 = 0
⇒ y2 = 4 ⇒ y = ±2
Hence the points are (1, 2), (1, -2).

Question 4.
Find the equation of the tangent to the curve y = $$\sqrt{3 x-2}$$ which is parallel to the line 4x – 2y + 5 = 0.
Slope of the line 4x – 2y + 5 = 0 is 2.

acceptable since y is positive.
Hence the point is $$\left(\frac{41}{48}, \frac{3}{4}\right)$$
Equation of tangent is;

⇒ 6(4y – 3) = (48x – 41)
⇒ 24y – 18 = 48x – 41
⇒ 48x – 24y – 23 = 0.

Question 5.
Prove that the curve x = y2 and xy = k cut at right angles, if 8k2 = 1.
x = y2 ___(1)
⇒ 1 = 2y $$\frac{d y}{d x}$$ ⇒ $$\frac{d y}{d x}$$ = $$\frac{1}{2y}$$
xy = 2k ___(2)
⇒ x $$\frac{d y}{d x}$$ + y.1 = 0 ⇒ $$\frac{d y}{d x}$$ = $$-\frac{y}{x}$$
The product of the slopes will be – 1.

Question 6.
The gradient at any point (x, y) of a curve is 3x2 – 12 and the curve through the point (2, -7).

1. Find the equation of the tangent at the point ( 2, -7 ). (2)
2. Find the equation to the curve. (2)

1. Given gradient as 3x2 – 12 ⇒ $$\frac{d y}{d x}$$ = 3x2 – 12
Slope at (2, -7) is given by
$$\left(\frac{d y}{d x}\right)_{x=2}$$ = 3(2)2 – 12 = 0
Since slope is zero, the tangent is parallel to x – axis.
Here y = – 7 is the equation of the tangent at (2, -7).

2. Given, $$\frac{d y}{d x}$$ = 3x2 – 12
⇒ ∫dy = ∫(3x2 – 12 )dx
y = 3$$\frac{x^{3}}{3}$$ – 12x + c ⇒ y = x3 – 12x + c ____(1)
Given (2, -7) is a point on the curve.
(1) ⇒ -7 = (2)3 – 12(2) + c ⇒ -7 = 8 – 24 + c ⇒ c = 9
∴ Curve is y = x3 – 12x + 9.

Question 7.
Consider the curve x2/3 + y2/3 = 2

1. Find the slope of the tangent to the curve at the point (1, 1). (2)
2. Find the equation of the normal at the point (1, 1). (2)

1. Given, x2/3 + y2/3 = 2,
Differentiating w.r.t. x,

⇒ slope of tangent = – 1.

2. Slope of normal = $$-\frac{1}{-1}$$ = 1.
Equation of the normal is
y – 1 = 1(x – 1) ⇒ y – x = 0.

Question 8.
Find the intervals in which the function f given by f(x) = 2x3 – 3x2 – 36x + 7 is

1. Strictly increasing. (2)
2. Strictly decreasing. (2)

Given; f(x) = 2x3 – 3x2 – 36x + 7
⇒ f'(x) = 6x2 – 6x – 36
f'(x) = 0 ⇒ 6x2 – 6x – 36 = 0
⇒ 6(x2 – x – 6) = 0
⇒ 6(x + 2)(x – 3) = 0 ⇒ x = -2, 3
The intervals are (-∞, -2),(- 2, 3), (3, ∞)
f'(-3) = 6(-3 + 2)(-3 – 3) > 0.
∴ Strictly increasing in (-∞, -2).
f'(0) = 6(2)(-3) < 0.
∴ Strictly decreasing in (- 2, 3).
f'(4) = 6(4 + 2)(4 – 3) > 0
∴ Strictly increasing in (3, ∞).

Question 9.
Use differentials to find the approximate value of $$\sqrt{0.6}$$ up to 3 places of decimals.
Take y = $$\sqrt{x}$$, let x = 0.64 and ∆x = -0.04
Then; f(x) = y = $$\sqrt{x}$$
f(x + ∆x) = y + ∆y

(1) ⇒ $$\sqrt{0.6}$$ = 0.8 – 0.025 = 0.775.

Question 10.
Use differentials to find the approximate value of (0.999)$$\frac{1}{10}$$ up to 3 places of decimals.
Take = x$$\frac{1}{10}$$, let x = 1 and ∆x = -0.001
Then; f(x) = y
f(x + ∆x) = y + ∆y
(0.999)$$\frac{1}{10}$$ = x$$\frac{1}{10}$$ + ∆y
(0.999)$$\frac{1}{10}$$ = (1)$$\frac{1}{10}$$ + ∆y
⇒ (0.999)$$\frac{1}{10}$$ = 1 + ∆y ______(1)

(1) ⇒ (0.999)$$\frac{1}{10}$$ = 1 – 0.0001 = 0.9999.

Question 11.
Use differentials to find the approximate value of (15)$$\frac{1}{4}$$ up to 3 places of decimals.
Takey = x$$\frac{1}{4}$$, let x = 16 and ∆x = -1
Then; f(x) = y
f(x + ∆x) = y + ∆y
(15)$$\frac{1}{4}$$ = x$$\frac{1}{4}$$ + ∆y
(15)$$\frac{1}{4}$$ = 16$$\frac{1}{4}$$ + ∆y
(15)$$\frac{1}{4}$$ = 2 + ∆y ____(1)
⇒ ∆y ≈ dy = $$\frac{d y}{d x}$$ ∆x

Question 12.
Use differentials to find the approximate value of (26.57)$$\frac{1}{3}$$ up to 3 places of decimals.
Take y = x$$\frac{1}{3}$$, let x = 27 and ∆x = -0.43
Then; f(x) = y
f(x + ∆x) = y + ∆y
f(x + ∆x) = f(x) + ∆y
(26.57)$$\frac{1}{3}$$ = 27$$\frac{1}{3}$$ + ∆y .
⇒ (26.57)$$\frac{1}{3}$$ = 3 + ∆y ____(1)

(1) ⇒ (26.57)$$\frac{1}{3}$$ = 3 – 0.016 = 2.984.

Question 13.
Find the approximate value of f(5.001) where f(x) = x3 – 7x2 + 15
Let x = 5 and ∆x = 0.001
Then; f(x) = y
f(x + ∆x) = y + ∆y
f (5.001) = f(x) + ∆y
f(5.001) = f(5) + ∆y
f(5.001) = 53 – 7(5)2 + 15 + ∆y
⇒ f(5.001) = -35 + ∆y …
⇒ ∆y ≈ dy = $$\frac{d y}{d x}$$ ∆x ⇒ dy = (3x2 – 14x) × 0.001
= (3(5)2 – 14(5)) × 0.001 = (75-70)0.001 = 0.005
(1) ⇒ f(5.001) = -35 + 0.005 = -34.995.

Question 14.
Find the approximate value of f(3.02) where f(x) = 3x2 + 5x + 3
Let x = 3 and ∆x = 0.02
Then; f(x) = y
f(x + ∆x) = y + ∆y
f(3.02) = f(x) + ∆y
f(3.02) = f(3) + ∆y
f(3.02) = 3(3)2 + 5(2) + 3 + ∆y
⇒ f(3.02) = 45 + ∆y ____(1)
⇒ ∆y ≈ dy = $$\frac{d y}{d x}$$ ∆x ⇒ dy = (6x + 5) × 0.02
= (6(3) + 5) × 0.02 = (18 + 5)0.02 = 0.46
(1) ⇒ f(3.02) = 45 + 0.46 = 45.46.

Question 15.
Consider the function y = f$$\sqrt{x}$$

1. If x = 0.0036 and ∆x = 0.0001 find ∆y. (3)
2. Hence approximate $$\sqrt{.0037}$$ using differentials. (1)

1. Let x = .0036, ∆x = 0.0001

2. (1) ⇒ $$\sqrt{.0037}$$ = .000833 + .06 = .060833.

Question 16.
Find the approximate value of $$\sqrt[3]{124}$$.
f(x) = $$\sqrt[3]{x}$$ = x1/3 ⇒ f1(x) = 1/3x-2/3 = $$\frac{1}{3 x^{2 / 3}}$$
Let x = 125, ∆x = -1
Then; f(x) = y

Question 17.
Find two numbers x and y such that their sum is 35 and the product is x2 y5 a maximum.
Given; x + y = 35 ⇒ y = 35 – x
P = x2 y5 ⇒ P = x2(35 – x)5
⇒ p’ = 2x(3 5 – x)5 + x2 5(35 – x)4(-1)
⇒ P’ = x(35 – x)4[2(35- x) – 5x]
⇒ p’ = x(35 – x)4[70 – 7x]
⇒ p’ = 7x(35 – x)4[10 – x]
⇒ p” = 7[x(3 5 – x)4 [-1] + x(10 – x)4(35 – x)3 (-1) + (35 – x)4(10 – x)]
For turning points P’ = 0
⇒ 7x(35 – x)4[10 – x] = 0
⇒ x = 0, 35, 10
x = 0, 35 can be rejected since correspondingly y will be y = 35, 0
⇒ P” = 7[10(35 – 10)4[-1]] < 0
Therefore maximum at x = 10
Thus the numbers are 10 and 35 – 10= 10.

Question 18.
Using differentials, find the approximate value of (63)1/3.
Take y = x$$\frac{1}{3}$$, let x = 64 and ∆x = 1
Then; f(x) = y
f(x + ∆x) = y + ∆y

Question 19.

1. Find the point on the curve y = x3 – 10x + 8 at which the tangent is parallel to the line y = 2x + 1. (2)
2. Is the given line tangent to the curve? Why?

1. $$\frac{d y}{d x}$$ = 3x2 – 10
Slope of the line y = 2x +1 is 2
⇒ 3x2 – 10 = 2 ⇒ 3x2 = 12 ⇒ x = ±2
When x = 2
y = 23 – 10 × 2 + 8 = 8 – 20 + 8 = -4
When x = – 2
y = (-2)3 -10 × (-2) + 8 = -8 + 20 + 8 = 20
Therefore the points are (2, -4); (-2, 20)

2. No. Since (2, -4); (-2, 20) does not satisfies the equation y = 2x +1.

Question 20.
Suppose that a spherical balloon is inflated and it has volume ‘v’ and radius ‘r’ at time ‘t’.

1. If the balloon is inflated by pumping 900c.c. of gas per second. Find the rate a which the radius of the balloon is increasing when the radius is 15 cm. (2)
2. Find the rate of change of its surface at the instant when it radius is 15 cm. (2)

1. Let V be the volume of the sphere of radius r.
V = $$\frac{4}{3}$$ πr3, given; $$\frac{d V}{d t}$$ = 900, r = 15
Differentiating w.r.t t,

2. Let ‘s’ denote the surface area of the balloon, then
S = 4πr2
Differentiating, $$\frac{d s}{d t}$$ = 4π.2r.$$\frac{d r}{d t}$$ =8.π r .$$\frac{d r}{d t}$$
= 8π × 15 × $$\frac{1}{\pi}$$ = 120 cm2/sec.

Question 21.
Use differentials to find the approximate value of (0.009)$$\frac{1}{3}$$ up to 3 places of decimals.
Take y = x$$\frac{1}{3}$$, let x = 0.008 and ∆x = 0.001
Then; F(x) = Y
f(x + ∆x) = y + ∆y

Question 22.
Find the approximate value of $$\sqrt{401}$$.
f(x) = $$\sqrt{x}$$ = x1/2
f'(x) = $$\frac{1}{2 \sqrt{x}}$$
Let x = 400 ∆x = 1
f(x) = y = $$\sqrt{x}$$
f(x + ∆x) = y + ∆y

Question 23.
Consider y = $$\frac{\log x}{x}$$, in (0, ∞)

1. Find the value of x at which $$\frac{d y}{d x}$$ = 0 (2)
2. Find the maximum value.

1.

2.

∴ y is maximum when x = e.
The maximum value is $$\frac{1}{e}$$.

Question 24.
Find the point on the curve y = x3 – 11x + 5 at which the tangent is y = x – 11.
Slope of the line y = x – 11 is 1.
Given; y = x3 – 11x + 5 ⇒ $$\frac{d y}{d x}$$ = 3x2 – 11 = 1
⇒ 3x2 = 12 ⇒ x = ±2
At x = 2, ⇒ y = x – 11 = 2- 11 = -9
⇒ (2, -9)
At x = -2, ⇒ y = x – 11 = -2 – 11 = -13
⇒ (-2, -13)
But the point (-2, -13) do not lie on the curve, hence the point is (2, -9).

Question 25.
Consider the curve y = x2 – 2x + 7

1. Find the slope of the tangent of the curve at x = 2. (2)
2. Write down the equation of the tangent at x =2. (2)

1. Given, y = x2 – 2x + 7 ⇒ y’ = 2x – 2
(y’)x=2 = 2(2) – 2 = 2.

2. At x = 2 , y = 22 – 2(2) + 7 = 7.
Equation of the tangent at (2, 7) is
y – 7 = 2(x – 2) ⇒ 2x – y + 3 = 0.

Question 26.
Find the absolute maximum value and minimum value of the following functions.

1. f(x) = 2x3 – 15x2 + 36x + 1, x ∈ [1, 5]
2. f(x) = 12x$$\frac{4}{3}$$ – 6x$$\frac{1}{3}$$, x ∈ [-1, 1]

1. Given; f(x) = 2x3 – 15x2 + 36x + 1, x ∈ [1, 5]
⇒ f'(x) = 6x2 – 30x + 36
For turning point f'(x) = 0 ⇒ 6x2 – 30x + 36 = 0
⇒ x2 – 5x + 6 = 0 ⇒ (x -3)(x – 2) = 0
⇒ x = 3, 2
f(1) = 2(1)3 – 15(1)2 + 36(1) + 1 = 24
f(2) = 2(2)3 – 15(2)2 + 36(2) + 1 = 29
f(3) = 2(3)3 – 15(3)2 + 36(3) + 1 = 28
f(5) = 2(5)3 – 15(5)2 + 36(5) + 1 = 56
Absolute maximum = max {24, 29, 28, 56} = 56
Absolute minimum = min {24, 29, 28, 56} = 24

2. Given;

f'(x) = 0 at x = $$\frac{1}{8}$$ and f'(x) is not defined at x = 0. Therefore;

Absolute maximum = max {18, 0, 6, $$-\frac{9}{4}$$} = 18
Absolute minimum = min {18, 0, 6, $$-\frac{9}{4}$$} = $$-\frac{9}{4}$$.

Question 27.
Consider the function y = x3 – 6x2 + 3x – 1

1. Find the slope at x= -1. (1)
2. Find the minimum gradient of the above curve. (3)

1. Given,
y = x3 – 6x2 + 3x – 1 ⇒ y’ = 3x2 – 12x + 3
Gradient at (x = -1) = (y’)x=1 = 3(-1)2 – 12(-1) + 3 = 18.

2. Now for minimum gradient we have to apply maxima – minima condition to the function y’ .ie, y” = 6x – 12 , for turning points of y’ is given by y” = 0.
Therefore, 6x – 12 = 0 ⇒ x = 2
Now, y”’ = 6 > 0
∴ y’ is maximum at x = 2.
Minimum gradient at (x = 2) is
= 12 – 24 + 3 = – 9.

### Plus Two Maths Application of Derivatives Six Mark Questions and Answers

Question 1.
A curve passes through the origin, and its gradient function is 2x – $$\frac{x^{2}}{2}$$

1. Find its y coordinate when x= 2. (4)
2. Find the equation of the tangent at x= 2. (2)

Given;

Integrating we have; ∫dy = ∫(2x – $$\frac{x^{2}}{2}$$)dx
⇒ y = x2 – $$\frac{x^{3}}{6}$$ + c ___(1)
Since the curve passes through (0, 0)
(1) ⇒ 0 = 0 + c ⇒ c = 0
∴ Equation of the curve is y = x2 – $$\frac{x^{3}}{6}$$
When x = 2 ⇒ y = 22 – $$\frac{2^{3}}{6}$$ = $$\frac{8}{3}$$
∴ coordinate is (2, $$\frac{8}{3}$$).

2. Slope at (2, $$\frac{8}{3}$$) = 2 × 2 – $$\frac{2^{2}}{2}$$ = 2
∴ Equation of the tangent at (2, $$\frac{8}{3}$$) is given by
y – $$\frac{8}{3}$$ = 2(x – 2) ⇒ 3y – 8 = 6x – 12 ⇒ 3y = 6x – 4.

Question 2.
(i) Choose the correct answer from the bracket. The slope of the tangent to the curve y = x3 – 2x + 3 at x = 1 is ____(1)
(a) 0
(b) 1
(c) 2
(d) 3
(ii) Find points on the curve $$\frac{x^{2}}{25}+\frac{y^{2}}{9}$$ = 1 at which the tangents are (2)
(a) Parallel to x-axis
(b) parallel to y – axis.
(iii) Use differential to approximate $$\sqrt{25.6}$$. (3)
(i) (b) 1, Since

(ii)

(a) $$\frac{d y}{d x}$$ = 0, since tangents are parallel to x- axis.
$$\frac{-9x}{25}$$ = 0, x = 0 ∴ y = ± 3;
The points are (0, 3) and (0, -3)

(b) $$\frac{-25 y}{9 x}$$ = 0, since tangents are parallel to y-axis, slope of normal = 0; y = o
∴ x = ± 5
The points are (5, 0) and (-5, 0)

(iii) Take y = $$\sqrt{x}$$ , let x = 25 and ∆x = 0.6
Then; f(x) = y = $$\sqrt{x}$$
f(x + ∆x) = y + ∆y

Question 3.
Let x and y be the length and breadth of the rectangle ABCD in a circle having radius r. Let ∠CAB = θ (Ref. figure). If ∆ represent area of the rectangle and r is a constant.

1. Write ∆ in terms of r and θ. (2)
2. Find $$\frac{d \Delta}{d \theta}$$ and $$\frac{d^{2} \Delta}{d \theta^{2}}$$. (1)
3. Hence find the maximum value of ∆. (2)
4. Show that the rectangle of maximum area that can be inscribed in a circle of radius r is a square of side $$\sqrt{2} r$$. (1)

1. Area of the rectangle is ∆ = xy
From the figure y = 2r sinθ, x = 2r cosθ
∆ = xy = 4r2sinθcosθ = 2r2sin2θ

2. $$\frac{d \Delta}{d \theta}$$ = 4r2 cos2θ ⇒ $$\frac{d^{2} \Delta}{d \theta^{2}}$$ = -8r2sin2θ

3. For turning points

Therefore local maximum at θ = $$\frac{\pi}{4}$$

4. Then;

Hence the rectangle becomes a square.

Question 4.
The second derivative of the equation of a curve is given by the equation x $$\frac{d^{2} y}{d x^{2}}$$ = 1, given y = 1, $$\frac{d y}{d x}$$ = 0 when x= 1.

1. Find the slope at x = e. (2)
2. Find the equation of the curve. (2)
3. Find the equation of the normal at x= e. (2)

1. Given;

Integrating we get,

∴ Slope of the curve at x = e is given by
$$\left(\frac{d y}{d x}\right)_{x=e}$$ = loge = 1.

2. We have,
$$\frac{d y}{d x}$$ = logx, ⇒ dy = logxdx
Integrating we get,
∫dy = ∫logx dx ⇒ y = logx.x – ∫$$\frac{1}{x}$$.x dx + c2
⇒ y = xlogx – x + c2 ____(2)
Given; y = 1 when x = 1
(2) ⇒ 1 = 1log1 – 1 + c2 ⇒ 1 = 0 – 1 + c2 ⇒ c2 = 2
Therefore the equation of the curve is
y = xlogx – x + 2

3. We have, y = xlogx – x + 2
When x = e
⇒ y = e log e – e + 2 ⇒ y = e – e + 2 = 2
So we have to find the slope at (e, 2),
We know; $$\left(\frac{d y}{d x}\right)_{x=e}$$ = log e = 1
∴ Slope of the normal at (e, 2)= -1
∴ Equation of the normal at (e, 2) is.
y – 2 = (-1) (x – e)
y – 2 = – x + e ⇒ y + x = e + 2.

Question 5.
The given figure represents a cylinder Inscribed in a sphere.

1. Find an expression for the volume V of the cylinder. (2)
2. Find the height of the cylinder when its volume V is maximum. (2)
3. Find the volume and radius of the largest cylinder. (2)

1. From the right triangle ∆OAB,
y2 = R2 – x2 ⇒ y = $$\sqrt{R^{2}-x^{2}}$$
Which is the radius of the cylinder
Also height = 2 x
∴ Volume = V= π y2 × 2x = 2π(R2 – x2)x = 2π(R2x – x3).

2. Now,

For maximum or minimum,

Question 6.
If f(x) = x3 + 3x2 – 9x + 4 is a real function

1. Find the intervals in which the function is increasing or decreasing. (3)
2. Find the points of local maxima or local minima of f(x) (2)
3. Graph of a function is given in the following figure:

Which among the following represents the graph of its derivative? (1)

1. f'(x) = 3x2 + 6x – 9
For turning points f'(x) = 3x2 + 6x – 9 = 0
⇒ x = 1, -3
These turning point divide the domain of f(x) in the following intervals. (-∞, -3), (-3, 1), (1, ∞) in (-∞, -3)
⇒ f'(-4) = 3(-4)2 + 6(-4) – 9 > 0
Hence increasing.
In (-3, 1) ⇒ f'(0) = 3(0)2 + 6(0) – 9 < 0
Hence decreasing.
In (1, ∞) ⇒ f'(2) = 3(2)2 + 6(2) – 9 > 0
Hence increasing.

2. x = -3 is a local maximum point and x = 1 is a local minimum point.

3. (a)

The function passes through origin and has a local maximum at x = 2.

Question 7.
Of all the Cylinders with given surface area, show that the volume is maximum when height is equal to the diameter of the base.
Let r be the radius, h be the height, V be the volume and S be the surface area
S = 2πr2 + 2 πrh

S – 6πr2 = 0
2πr2 + 2πrh – 6πr2 = 0
So h = 2r
So volume is maximum when h = 2r.

Question 8.
Sand is pouring from a pipe. The falling sand forms a Cone on the ground in such a way that the height of the Cone is always one-sixth of the radius of the base.

1. Establish a relation between the volume ‘v’ and height ‘h’ of the Cone using the given condition. (2)
2. lf the sand is pouring at the rate of -12 cm/sec, Find the rate of change of height of the Cone. (2)
3. Find $$\frac{\mathrm{dh}}{\mathrm{dt}}$$ when h = 4cm. (2)

1. Given that the height of the Cone is one-sixth of the radius of the base, then h = $$\frac{r}{6}$$ ⇒ r = 6h
Then Volume V = $$\frac{1}{3}$$ πr2h = $$\frac{1}{3}$$ π(6h)2.h
V = $$\frac{1}{3}$$ π 36h2.h = $$\frac{1}{3}$$ π 36h3
V =12 πh3 ____(1)

2. Differentiating (1) we get

3. When h = 4 cm

Question 9.
(i) Choose the correct answer from the bracket. The rate of change of the area of a circle with respect to its radius r at r = 10cm is.
(a) 10π
(b) 20π
(c) 30π
(d) 40π (1)
(ii) Find the intervals in which the function f given by f(x) = x2 – 6x + 5 is (2)
(a) Strictly increasing
(b) Strictly decreasing
(iii) Find the local minimum and local maximum value, if any, of the function f(x) = x3 – 6x2 + 9x + 8 (3)

(ii) f'(x) = 2x — 6; 2x – 6 = 0; x = 3
(-∞, 3 ) is strictly decreasing
(3, ∞) is strictly increasing.

(iii) f'(x) = 3x2 – 12x + 9
f11 = 6x — 12
For maxima, minima
f1 = 0 → 3x2 – 12x + 9 = 0
3(x – 3)(x — 1) = 0; x = 3, x = 1
At x = 3 f11(x) = 6 × 3 – 12 = 18 – 12 = 6 > 0
f is minimum, the local minimum value of f = 8
At x = 1 f11(x) = 6 × 1 – 12 = -6 < 0,
f is maximum, the local maximum value of f = 12.

Question 10.
A wire of length 28m is cut into two pieces. One of the pieces is be made into a square and the other into a circle. What should be the length of the two pieces so that combined area of the square and the circle is minimum using differentiation?
Let the length of one piece be ‘x’ and other piece be ‘28 – x’. Let from the first piece we will make a circle of radius Y and from the second piece we will make a square of side y. Then,

Let A be the combined area of the circle and square, then

Question 11.
An open box of maximum volume is to be made from a square piece of tin sheet 24cm on a side by cutting equal squares from the corners and turning of the sides.
(i) Complete the following table. (2)

(ii) Using the above table, express V as a function of x and determine its domain. (1)
(iii) Find height (x. cm) of the box when volume V is maximum by differentiation. (3)
(i)

(ii) Generalise the above table as a function.
V = x(24-2x)2, 0 < x < 12.

(iii) $$\frac{d V}{d x}$$ = x.2(24 – 2x)(-2) + (24 – 2x)2
= -4x(24 – 2x) + (24 – 2x)2
= -96x + 8x2 + 576 + 4x2 – 96x
= 12x2 – 192x + 576
For maximum or minimum,

Therefore volume is maximum when x = 4 cm.

Question 12.
A square tank of capacity 250 m3 has to be dug out. The cost of land is Rs. 50 per m2. The cost of digging increases with the depth and for the whole tank is Rs. 400 × (depth)2.

1. Find an expression for the cost of digging the tank. (3)
2. Find the dimension of the tank when the total cost is least. (3)

1. Let x, x and y be the length, breadth, and depth of the tank.
Then, V = x. x. y = 250 ⇒ y = $$\frac{250}{x^{2}}$$.
Area of land = x2
⇒ Cost of land = 50 x2
(∵ cost of land is Rs.50/m2)
Cost of digging = 400 × (depth)2 = 400 × (y)2
∴ Total cost = C = 50 x2 + 400 × (y)2

2. We have, C = 50x2 + $$\frac{400 \times(250)^{2}}{x^{4}}$$.
Differentiating w.r.t.x, we get,

∴ Maximum at x = 10
m ⇒ when x = 10m and
y = $$\frac{250}{10^{2}}$$ = 2.5m the total cost is least.

Question 13.
Show that the right circular cone of least curved surface and given volume has an altitude equal to $$\sqrt{2}$$ times the radius of the base.
Volume of the cone will be, V =$$\frac{1}{3}$$πr2h
h = $$\frac{3 V}{\pi r^{2}}$$ ____(1)
Curved surface area will be, S = πrl
⇒ S2 = π2r2l2 = P
⇒ P = π2r2(h2 + r2) ⇒ P = π2r2h2 + π2r4)

⇒ 2r2 = h2 ⇒ h = $$\sqrt{2} r$$.

Question 14.
Let ABC be an isosceles triangle inscribed in a circle having radius r. Then by figure, area of the triangle ABC is ∆

1. Find $$\frac{d \Delta}{d \theta}$$ and $$\frac{d^{2} \Delta}{d \theta^{2}}$$ (2)
2. Find the maximum value of ∆. (3)
3. Show that the isosceles triangle of maximum area that can be in scribed in a given circle is an equilateral triangle. (1)

1. Area of the isosceles triangle is ∆ = $$\frac{1}{2}$$bh
From the figure b = r sin2θ, h = r + r cos2θ

2. For turning points

Therefore local maximum a θ = $$\frac{\pi}{6}$$ which means the area of the isosceles triangle is maximum When θ = $$\frac{\pi}{6}$$.

3. Then; ∠OCB = 30° ⇒ ∠ACB = 2∠OCB = 60°. Therefore the isosceles triangle is an equilateral triangle.

Question 15.
(i) Using the graph of the function f (x) in the interval [ a, h ] match the following.

 A – Point B – Nature x = a Absolute maximum x = b Absolute minimum x = e Local maximum x = d Local minimum Point of inflexion.

(ii) Consider the function f(x) = 3x4 – 8x3 + 12x2 – 48x + 25
(a) Find the turning points of f(x). (1)
(b) Explain the nature of the turning points (1)
(c) Find the absolute extreme values of f(x). (2)
(i)

 A – Point B – Nature x = a Absolute minimum x = b Local maximum x = e Point of inflexion x = d Absolute maximum

(ii) (a) f(x) = 12x3 – 24x2 + 24x – 48
For turning points,
f'(x) = 0 ⇒ 12x3 – 24x2 + 24x – 48 = 0
⇒ x3 – 2x2 + 2x – 4 = 0
⇒ (x2 + 2)(x – 2) = 0 ⇒ x = ± ($$\sqrt{-2}$$, 2)
We admit only x = 2 as x = $$\sqrt{-2}$$ is not a real number.
Therefore at x = 2 f (x) has a turning point.

(b) f”(x) = 36x2 – 48x + 24
⇒ f”(2) = 36(2)2 – 48 × 2 + 24 > 0
Therefore at x = 2 f(x) has a local minimum.

(c) f(0) = 25,
f(2) = 3(2)4 – 8(2)3 + 12(2)2 – 48 × 2 + 25 = -39
f(3) = 3(3)4 – 8(3)3 + 12(3)2 – 48 × 3 + 25 = 16
Consider the set { f (0), f{2), f (3)}
⇒ {25, -39, 16}
The maximum value of the above set is the absolute maximum and it is 25 at x = 0. The minimum value of the above set is the absolute minimum and it is -39 at x = 2.

Question 16.
An open box with a square base is to be made out of a given quantity of sheet of area a2.

1. If the box has side x units, then show that volume V= $$\frac{a^{2} x-x^{3}}{4}$$ (2)
2. Show that the maximum volume is $$\frac{a^{3}}{6 \sqrt{3}}$$ (4)

1. Area = a2 = x2 + 4xh,
h = height of the box.

2. We have,

Question 17.
For the function f(x) = sin2x, 0 < x < π
(i) Find the point between 0 and π that satisfies f'(x) = 0. (2)
(ii) Find the point of local maxima and local minima. (2)
(iii) Find the local maximum and local minimum value. (2)

Question 18.
A cylindrical can with a volume of 125m3 (about 2 litres) is to be made by cutting its top and bottom from metal squares and forming its curved side by bending a rectangular sheet of metal to match its ends. What radius ‘r’ and height ‘h’ of the can will minimize the amount of material required.

The circular top and bottom should be cut out from a square metal sheet of side 2r. Therefore the area of squares is 8r2.
Area A = 8r2 + 2πrh

∴ To minimize the amount of material, r = 2.5
$$h=\frac{125}{\pi(2.5)^{2}}=6.3$$.

Question 19.
A rectangle sheet of tin with adjascent sides 45cm and 24cm is to be made into a box • without top, by cutting off equal squares from the comers and folding up the flaps

1. Taking the side of the square cut off as x, express the volume of the box as the function of x. (2)
2. For what value of x, the volume of the box will be maximum. (4)

1. Length of the box = 45 – 2x
Breadth of the box = 24 – 2x
Height of the box = x
Volume; V = (45 – 2x)(24 – 2x)x
= (1080 – 138x + 4x2)x
= 4x3 – 138x2 + 1080x.

2. $$\frac{d y}{d x}$$ = 12x2 – 276x + 1080

12x2 – 276x + 1080 = 0
x2 – 23x + 90 = 0
x = 18, 5
x = 18 is impossible
∴ x = 5 when x = 5, $$\frac{d^{2} y}{d x^{2}}$$ < 0

The volume of the box is maximum at x = 5.

## Plus Two Accountancy Chapter Wise Questions and Answers Chapter 4 Graphs and Charts for Business Data

Students can Download Chapter 4 Graphs and Charts for Business Data Questions and Answers, Plus Two Accountancy Chapter Wise Questions and Answers helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

## Kerala Plus Two Chemistry Chapter Wise Questions and Answers Chapter 4 Graphs and Charts for Business Data

### Plus Two Accountancy Graphs and Charts for Business Data One Mark Questions and Answers

Question 1.
_____________ are the visual representation of numerical data
Chart/ Graph

Question 2.
Chart / Graph has at least ____________ dimenstional relationship
(a) Two
(b) Three
(c) Four
(d) Five
(a) Two

Question 3.
____________ chart is suitable for comparing multiple.
Bar Chart

Question 4.
In column chart, the X-axis shows
(a) Value of each category
(b) Different categories
(c) Height of the chart
(d) Depth of the value
(b) Different categories

Question 5.
________ Chart is similar to the column chart, with the difference being that the data series are displayed horizontally
(a) Line chart
(b) Pie chart
(c) Barchart
(d) Area chart
(c) Bar chart

Question 6.
________ chart shows data changes for a certain period of time.
Line chart

Question 7.
_______ chart contains only one data series
Pie chart

Question 8.
_______chart shows values as circular sectors to the total circle
Pie chart

Question 9.
Pie chart don’t have more than __________ categories.
(a) Ten
(b) Twenty Five
(c) Seven
(d) Three
(c) Seven

Question 10.
____________ is a pictorial representation of data, which has at least two dimensional relationships.
(a) Graph
(b) Chart
(c) Diagram
(d) All the above
(d) All the above

Question 11.
_________ Chart is used to compare values across categories.
(a) Column chart
(b) Line chart
(c) Pie chart
(d) Barchart
(a) Column chart

Question 12.
_________ chart is used to display trends over time.
Line chart

Question 13.
The entire chart including all elements is termed as ________
Chart area

Question 14.
In 3D chart, the area is bounded by three axes ie _____, _____ & _____
X, Y, Z

Question 15.
In ______ chart, both axes display values ie they have no category axis.
XY Chart or Scatter diagram

Question 16.
_______ specifices the colour, symbol or pattern used to mark data series.
Legends

Question 17.
The change the location of a chart, right click the chart and select.
(a) Chart Type
(b) Source Data
(c) Move here
(d) Chart Options
(c) Move here

Question 18.
In 3D chart X, Y & Z axes are used to show
(a) Category, Value, Total
(b) Depth, Vertical, Horizontal
(d) Category, Value, Series.
(d) Category, Value, Series

Question 19.
Legand can be repositioned on the chart
(a) Anywhere
(b) On right side only
(c) On the corner only
(d) On the left side only
(a) Anywhere

Question 20.
Which chart element details the data values and categories below the chart?
(a) Data table
(b) Data marker
(c) Data labels
(d) Datapoint
(c) Data labels

Question 21.

Which type of chart is this?

Question 22.
The intersection of both the axis (X-axis and Y-axis) is called __________ of the graph.
Origin (0)

Question 23.
_________ Chart display in rings, where each ring represents a data series
Doughnut chart.

Question 24.
Name the given chart

Bar Chart

Question 25.
In _________ chart, the area below the plotted lines is solid
Area chart.

Question 26.
Radar chart / Net chart is also known as ______
(a) Doughnut chart
(b) Pie chart
(c) Ara chart
(d) Star chart
(d) Star chart

Question 27.
Which among the following is the special feature of 3D chart
(a) Chart area
(b) X & Y axes
(c) Chart wall
(d) Legend
(c) Chart wall

Question 28.
Give a suitable name to the diagram

(a) Barchart
(b) Single line graph
(c) Pie chart
(d) Area Chart
(c) Pie Chart

### Plus Two Accountancy Graphs and Charts for Business Data Two Mark Questions and Answers

Question 1.
Name the different chart formats in Libre Office Calc
Barchart, Column Chart, Pie chart, Line chart, Area chart, Doughnut chart, etc.

Question 2.
What is the importance of charts and graphs in business?

1. Chart and graphs covey lots of business information in a visual format
2. Different business Data variables plotted in charts and graphs show the trend of the business in an easy way

Question 3.
Identify the type of chart

Line chart

Question 4.
Give a short note on it.

1. Barchart
2. Pie chart

1. Bar Chart
This type of chart shows a bar graph or column chart with horizontal bars. The Y-axis shows categories and the X-axis shows the value for each category. It is suitable for comparing multiple values.

2. Pie chart
A pie chart displays the contribution of each value to a total. It represents multiple subgroup of a single variable. It contains only one data series. A pie chart shows values as circular sectors of the total circle. Pie chart may be

• Normal Pie chart
• Exploded Pie chart
• Doughnut chart or Donut chart
• Exploded Doughnut chart

Question 5.
What are the special features of graphs and charts?

1. Graphs/charts are the pictorial representation of business data
2. A chart represents tabular numeric data
3. Dimensions in the data are often displayed on axes (X, Y, & Z)

Question 6.
Differentiate between Chart area and Chart wall?
1. Chart area:
This is the total space that is enclosed by a chart. It is the background of the chart.

2. Chart wall:
In 2D chart, the wall or area is bounded by the X and Y-axis. In the 3D chart, the wall is bounded by three axes X, Y and Z

Question 7.
Quarterly sales of a business firm is used to create a bar graph. Identify the Data variables plotted on X and Y-axis
X-axis – Ist Quarter, IInd Quarter, IIIrd Quarter, IVth Quarter,
Y-axis – Sales in Ist Quarter, Sales in Ind Quarter, Sales in IIIrd Quarter, Sales in IVth Quarter

Question 8.
Identify the type of chart

(a) 2D Chart
(b) 3D Chart

Question 9.
What is the use of Auto shapes in LibreOffice Calc?
Auto shapes tool bar allows drawing a number of geometrical shapes, arrows; flow chart elements, etc.

Question 10.
What is PIE chart? What are the specialties of PIE chart.
Pie chart:
A pie chart displays the contribution of each value to a total. It represents multiple subgroup of a single variable. It contains only one data series. A pie chart shows values as circular sectors of the total circle. Pie chart may be

1. Normal Pie chart
2. Exploded Pie chart
3. Doughnut chart or Donut chart
4. Exploded Doughnut chart

Question 11.
Choose the right statements from the following.

1. We can put on the right side of the origin positive values and on left side of the origin negative values of data on X-axis
2. The upward side of origin shows postiive values and downward side of the origin shows negative values of data on Y-axis.
3. We can put on the right side of the origin negative values and on left side of the origin positive values of data on X-axis.
4. The upward side of origin shows negative values and downward side of the origin shows positive values of data on Y-axis.

Right statements a & b

Question 12.
Identify the type of given chart. List down its features.

1. It is a Doughnut chart
2. Features of the doughnut chart
• It displays data in rings
• Each ring represents a data series
• The first data series is displayed in the center of the chart

Question 13.
What is a 3-D chart?
Charts can be prepared with three dimensional (3-D) effects. 3- D charts have a third axis. The third axis is called as Z-axis. So a 3-D chart has the fol¬lowing dimensions.

1. Horizontal axis – Indicate the category – known as X-axis
2. Vertical axis – Indicate the derived values – known as Y-axis
3. Depth axis – Indicate the series – known as Z-axis

Question 14
Differentiate between Data Marker and Data series.
1. Data Marker:
Individual values plotted in a chart are called data marker or data point.

2. Data Series:
Data markers of the same colour or pattern is called data series.

Question 15.
Is there any difference between

1. A column chart and
2. A bar chart?

1. Column Chart:
It is the most commonly used chart type. It shows a bar chart or bar graph with vertical bars. The X-axis shows the categories and Y-axis shows the value for each category. Column chart are used to compare values across categories.

2. Bar Chart:
This type of chart shows a bar graph or column chart with horizontal bars. The Y-axis shows categories and the X-axis shows the value for each category. It is suitable for comparing multiple values.

### Plus Two Accountancy Graphs and Charts for Business Data Three Mark Questions and Answers

Question 1.
Match the following

 A B (a) Area chart (1). XY chart. (b) Barchart (2). Display contribution to a total. (c) Pie chart (3). Suited for comparing multiple values. (d) Scatter chart (4). Display differences between several sets of data over a period of time.

 A B (a) Area chart (1). Display differences between several sets of data over a period of time. (b) Barchart (2). Suited for comparing multiple values. (c) Pie chart (3). Display contribution to a total. (d) Scatter chart (4). XY chart.

Question 2.
What are the advantages of using Graph/ Chart?

1. It summarises a large data set in visual form
2. Charts or graphs can clarify trends better than do tables.
3. It helps to estimate key values at a glance
4. It shows each data category in a frequency distribution.
5. It permits a visual check of the accuracy and reasonableness of calculations
6. The charts and graphs allow the investigator to draw a valid conclusion.

Question 3.
What are the elements of a Chart/ Graph

 Chart elements Description 1. Axes Titles Mention the names or titles for X, Y and Z axes. 2. X, Y, & Z axes In 2D chart, the horizontal X-axis contains categories and the vertical Y-axis contains dependent values. In 3D chart, the Z-axis will also be there represents the depth which 3. Chart Area This is the total space that is enclosed by a chart. It is the background of the chart. 4. Chart wall In 2D chart, the wall or area is bounded by the X and Y-axis. In the 3D chart, the wall is bounded by three axes X, Y, and Z. 5. Chart floor The chart floor is the lower area in the 3D chart. 6. Main Title/ sub Title It is the explanatory heading of the chart. It identifies the purpose of a chart. 7. Data Marker Individual values plotted in a chart are called data marker or data point. 8. Data Series Data markers of the same colour or pattern is called data series. 9. Legend It is an identifier of a piece of information shown in the chart/ graph. The legends are assigned to the data series in a chart. 10. Data Label The value of the data series plotted in a chart is known as data label. 11. Grid Lines These are the vertical and horizontal lines that appear in a chart. It increases the readability of a chart.

Question 4.
How to use word Art styles to format text.

• Step 1: Click in the chart element that contains text to be changed.
• Step 2: Click on the format.
• Step 3: Click on word Art styles.
• Step 4: Choose suitable options related to text formating like text fill, text outlines, shadow, etc.

### Plus Two Accountancy Graphs and Charts for Business Data Four Mark Questions and Answers

Question 1.
What are the difference between 2D charts and 3D charts

 2D Chart 3D Chart (a) The chart represents business data with just two dimensions (a) The chart represents business data with three dimensions (b) The two dimensions are length and height (No width) (b) The Three dimensions are Length and Height and width (or depth) (c) There are X-axis and Y-axis (c) There is X-axis, Y-axis is and Z-axis (d) The shape of the chart may be in the form of Rectangle, Square, Triangle, Polygon, etc (d) The shape of the chart may be Cylinder, Cube, Pyramid, etc

Question 2.
List out the steps to Rotate a chart.

• Step 1. Select the plot area of the chart.
• Step 2. Click on the format tab.
• Step 3. Click on format selection.
• Step 4. Click on 3D Rotation and type a value of angle between 0° to 360° and then click close
• Step 5. Click on the chart area of the chart and click on format tab.
• Step 6. Click on shape effects and then click on Bevel and select a bevel option.

Question 3.
What are the different types of charts?

1. Column chart: column chart are used to compare values across categories
2. Line chart: Line charts are used to display trends over time
3. Pie chart: Pie charts display the contribution of each value to a total
4. Bar chart: Bar charts are best suited for comparing multiple values
5. Area chart: Area chart emphasis differences between several sets of data over a period of time.
6. Scatter chart: (XY chart) This chart compares pairs of values.
7. Radar chart: Display values relative to a centre point.
8. Doughnut chart: It shows the relationship of parts to a whole. This chart display data in rings, where each ring represents a data series.

1. Column Chart:
It is the most commonly used chart type. It shows a bar chart or bar graph with vertical bars. The X-axis shows the categories and Y-axis shows the value for each category. Column chart are used to compare values across categories.

2. Line Chart:
A line chart shows values in the Y-axis and categories in X-axis. The Y values of each data series is connected by a line. Line chart shows data changes for a certain period of time.

3. Pie chart:
A pie chart displays the contribution of each value to a total. It represents multiple subgroup of a single variable. It contains only one data series. A pie chart shows values as circular sectors of the total circle. Pie chart may be

• Normal Pie chart
• Exploded Pie chart
• Doughnut chart or Donut chart
• Exploded Doughnut chart

4. Bar Chart:
This type of chart shows a bar graph or column chart with horizontal bars. The Y-axis shows categories and the X-axis shows the value for each category. It is suitable for comparing multiple values.

5. Area chart:
The chart shows values as points on the Y-axis. The X-axis shows categories. The Y values of each data series are connected by a line. The area between each two lines is filled with a colour.

6. Scatter chart:
Scatter chart is also known as XY chart. In this type of chart, both axes display values. This chart is used to show the relationship among two variables.

It is also known as Net chart or Star chart. A radar chart has a separate axis for each category and the axes extend outward from the center of the chart. The value of each data point is plotted on the corresponding axis.

8. Doughnut chart:
Chart display in rings, where each ring represents a data series. The first data series is displayed in the centre of the chart.

Question 4.
Identify and explain the type of chart given below.

1. This is scatter chart or XY chart.
2. Features:
• Both axes display values (No category)
• This chart is used to show the relationship among two variables
• Generally this chart is used for scientific, statistical and engineering data

Question 5.
Match the following.

 A B (a) Legends (i) Background of the chart (b) Pie chart (ii) Specifices the colour, symbol or pattern used to mark data series (c) Grid Lines (iii) Displays the contribution of each value to a total (d) Chart Area (iv) Display lines at the major intervals on the category X-axis and/or Y-axis

• (a) – (ii);
• (b) – (iii);
• (c) – (iv);
• (d) – (i)

Question 6.
How can we change the format of a selected chart element?

• Step 1. Click anywhere in the chart.
• Step 2. Click format
• Step 3. Click format selection
• Step 4. Select a category (Fill border, style, etc)
• Step 5. Select formatting options

Question 7.
List down any four advantages of charts/ Graphs

1. It summarises a large data set in visual form
2. Charts or graphs can clarify trends better than do tables.
3. It helps to estimate key values at a glance
4. It shows each data category in a frequency distribution.
5. It permits a visual check of the accuracy and reasonableness of calculations
6. The charts and graphs allow the investigator to draw a valid conclusion.

Question 8.
What are the features of Charts/ Graphs in Libre Office Calc?

1. Chart is a graphical representation of data
2. They are visual representation of numerical data
3. Charts can be read more quickly than the raw data
4. A chart has at least two axes – X and Y

### Plus Two Accountancy Graphs and Charts for Business Data Five Mark Questions and Answers

Question 1.
What Pie Chart? What are the different types of Pie Chart?
Pie chart:
A pie chart displays the contribution of each value to a total. It represents multiple subgroups of a single variable. It contains only one data series. A pie chart shows values as circular sectors of the total circle. Pie chart may be

1. Normal Pie chart
2. Exploded Pie chart
3. Doughnut chart or Donut chart
4. Exploded Doughnut chart

Question 2.
Name the different elements of given chart.

• X-Axis Title
• Y-Axis Title
• Data label
• Main Title
• Legend
• X-Axis
• Y-Axis
• Data series

Question 3.
Write the steps of changing the chart type.

1. First select the chart by double-clicking on it. The chart should now be surrounded by a gray bonder
2. Right-click on the chart and choose chart type.
3. Select the replacement chart type.
4. Click on [OK]

Question 4.
Write the steps for preparing a chart in Libre Office Calc.

• Step 1: Enter the data in a worksheet with proper column and row titles
• Step 2: Select the range of data using the mouse
• Step 3: Click on Insert Tab → Object → Chart. Select a chart type from the “Choose a chart type” list in chart wizard window.
• Step 4: Naming chart, X-axis and Y-axis. Click on the chart → Right click → Insert titles (Names) → OK
• Step 5: Change the layout or styles of chart.
• Step 6: Show or hide a legend
• Step 7: Display or hide chart axes or gridlines
• Step 8: Move (resize) a chart
• Step 9: Save a chart

### Plus Two Accountancy Graphs and Charts for Business Data Practical Lab Work Questions and Answers

Question 1.
Draw an Area Chart from the following

Procedure:
Step 1 – Open a new blanks worksheet in LibreOffice Calc

Step 2 – Enter the above data as follows.

Step 3 – Select the range A1: D6 which is to be shown in the chart.

Step 4 – Click on Insert menu → Click on Chart → Chart wizard → Select Area Chart → Finish
Output:

Question 2.
Quarterly sales of a product are given below. Draw a bar diagram/bar chart

 Ist Quarter 25600 IInd Quarter 33400 IIIrd Quarter 28700 IVth Quarter 40400

Procedure:
Step 1 – Open a new blanks worksheet in LibreOffice Calc

Step 2 – Enter the above data as follows.

Step 3 – Select the range A1: B5 which is to be shown in the chart:

Step 4 – Click on Insert menu → Click on Chart → Chart wizard Click on Bar chart → Finish
Output:

Question 3.
Draw a 3D column chart from the following details.

 Year Result % 2010 98 2011 94 2012 100 2013 85 2014 90

Procedure:
Step 1 – Open a new blank worksheet in LibreOffice Calc.

Step 2 – Enter the following data in the respective cells.

Step 3-Select the range A1: B6, which is to be shown in the chart.

Step 4 – Click on Insert menu → Click on Chart → Chart wizard → Click on Column Chart → Tick 3D Look → Select Bar Charts → Finish.
Output:

Question 4.
The net profits of a firm for the last six years are given below. Draw a line chart.

 Year Net Profit 2009 125800 2010 238400 2011 186500 2012 154900 2013 251000 2014 300000

Procedure:
Step 1 – Open a new blank worksheet in LibreOffice Calc

Step 2 – Enter the following data in the respective cells

Step 3 – Select the range A1: B7, which is to be shown in the chart

Step4- Click on Insert menu → Click on Chart → Chart Wizard → Click on Line Chart → Finish
Output:

Question 5.
Enter the following data into a LibreOffice Calc worksheet and draw a 3D Pie chart.

 Item of Expenses Amount Stationery 4890 Tuition Fee 850 Medical Treatment 3260 Insurance premium 1580 Petrol 3500 Vegetables 700 Bank savings 8400 Charity 1200

Procedure:
Step 1 – Open a new blank worksheet in LibreOffice Calc.

Step 2 – Enter the data in respective cells.

Step 3 – Select the range A2: B9, which is to be shown in the chart

Step 4 – Click on Insert menu → Click on Chart → Chart wizard → Click on Pie Chart Tick on 3D Look → Finish
Output:

Question 6.
Sales for the first six months in 2 years are given below. Draw a scatter chart in a LibreOffice Calc works sheet

Procedure:
Step 1 – Open a blank worksheet in LibreOffice Calc.

Step 2 – Enter the data in the following cells.

Step 3 – Select the range A1: C7, which is to be shown in the chart

Step 4 – Click on → Insert menu Click on → Chart → Chart Wizard → Scatter Chart→ Finish
Output:

Question 7.
The production of different items in Oct. 2015 is listed below. Draw a Radar Chart

Procedure:
Step 1 – Open a blank worksheet in LibreOffice Calc.

Step 2 – Enter the data in the following cells.

Step 3 – Select the range A1: C6, which is to be shown in the chart

Step 4 – Click on → Insert menu → Click on Chart → Chart Wizard → Click on Radar Chart → Finish
Output:

Question 8.
The following table shows the number of students passed in the higher secondary examination. Draw a doughnut chart.

Procedure:
Step 1 – Open a blank worksheet in LibreOffice Calc.

Step 2- Enter the data in the following cells.

Step 3 – Select the range A1: D6, which is to be shown in the chart.

Step 4 – Click on → Insert menu → Click on Chart → Chart Wizard → Click on doughnut Chart → Finish.
Output:

## Plus Two Economics Chapter Wise Questions and Answers Chapter 6 Open Economy Macroeconomics

Students can Download Chapter 6 Open Economy Macroeconomics Questions and Answers, Plus Two Economics Chapter Wise Questions and Answers helps you to revise the complete Kerala State Syllabus and score more marks in your examinations

## Kerala Plus Two Economics Chapter Wise Questions and Answers Chapter 6 Open Economy Macroeconomics

### Plus Two Economics Open Economy Macroeconomics One Mark Questions and Answers

Question 1.
Name the ‘balancing item’ affecting the inability to record all international transactions accurately?
Errors and omissions

Question 2.
The amount of rupees required to buy one US\$ is known as ………….
(i) Rupee dollar exchange rate
(ii) Dollar rupee exchange rate
(iii) Real exchange rate
(iv) Real effective exchange rate
(i) Rupee dollar exchange rate

Question 3.
Which among the following is a component of BOP account?
(i) Current account
(ii) Capital account
(iii) Official reserve
(iv) All the above
(iv) All the above

Question 4.
WTO was formed in?
(i) 1948
(ii) 1964
(iii) 1991
(iv) 1995
(iv) 1995

Question 5.
If export > imports, it represents
(iv) None of these above

Question 6.
Which of the following would be an appropriate policy to reduce a Balance of Payment / Deficit.
(i) An increase in government spending.
(ii) A cut in the level of indirect taxes
(iii) An increase in interest rates
(iv) A decrease in interest rates
(iii) An increase in interest rates

### Plus Two Economics Open Economy Macroeconomics Two Mark Questions and Answers

Question 1.
How is the exchange rate determined under flexible exchange rate regime?
In case of flexible exchange rates, the exchange rate changes to clear the market to equate the demand for and supply of foreign exchange.

Question 2.
List two items of the capital account of balance of payment account?

1. Gold movement
2. Reserve, Monetary gold & SDR

Question 3.
When will balance of trade shows a deficit?
Balance of trade shows a surplus when exports are greater than imports. That is, Surplus balance of trade = Exports > Imports

Question 4.
Name two sources of demand for foreign exchange.
Two sources of demand for foreign exchange are:

1. To purchase goods and services from abroad.
2. To send gifts and grants to foreign countries.

Question 5.
The value of a country’s import of goods is ₹200 crore and value of export of goods is ₹250 crore. Find out its balance of trade.
Balance of trade = Value of exports – value of imports = 250 – 200 = ₹50 crore

Question 6.
Identify the items to be included to trade balance to get current account balance.

2. Net transfers

Question 7.
Identify the situation mentioned below.

1. Rupee-dollar exchange rate change from 45 to 50.
2. Rupee-dollar exchange rate changed from 45 to 43.

1. Depreciation
2. Appreciation

Question 8.
State the National Income identity for an open economy.
Y = C + IG + (X – M)
Where,

• Y = National Income
• C = Comsumption
• I = Investment
• G = Government spending
• X = Export
• M = Import

Question 9.
The consumption function and import function of an economy can be given as,
C = a + b.y
M = M + m.y Identity the letters

1. b
2. a
3. m

1. Marginal propensity to consume
2. Autonomous consumption
3. Marginal propensity to import

Question 10.
If MPC = 0.8, and increase in autonomous demand is 200, calculate multiplier and the national output.
MPC = b – c = 0.8
Therefore multiplier is
$$\begin{array}{l} {\frac{1}{1-C} \text { or } \frac{1}{1-b}} \\ {\text { i.e. } \frac{1}{1-0.8}=\frac{1}{0.2}} \\ {=5} \end{array}$$
National output is 5 × 200 = 1,000

Question 11.
Calculate the open economy multiplier if c = 0.5, m = 0.3. Increase in autonomous demand = 200

Question 12.
What happens to the aggregate demand due to

1. A leakage from the circular flow of income
2. A injection to the circular flow of income

AD falls due to the leakage from circular flow of income and AD increases due to injection in too the circular flow of income.

Question 13.
List out the expert of services from the following……..
(a) India buys a new technology from France
(b) A Japaneese tourist visits India
(c) An Indian student registers for a UK exam
(d) an Indian doctor going to work in the US.
b and d are examples of expert services from India.

Question 14.
Analyse the effect of the following on imports and exchange rate.

1. Appreciation of domestic currency.
2. Depreciation of domestic currency
3. Increase in foreign direct investment.
4. Increase in import duty.

1. Increase in Imports, Fall in Exchange Rate
2. Decrease in Imports, Rise in Exchange Rate
3. Increase in Imports, Fall in Exchange Rate
4. Decrease in Imports, Fall in Exchange Rate

### Plus Two Economics Open Economy Macroeconomics Three Mark Questions and Answers

Question 1.
Classify the following into visible and invisible.
Steel, computer software, shipping services, wheat, machinery, food articles, banking, IT- enabled services, crude oil, shipping, textiles, Online business.

 Visibles Invisibles Steel Shipping Services Textiles Banking Wheat IT Enabled Services Machinery Shipping Food Articles Insurance Crude Oil Online Business

Question 2.
Classify the following into current account and capital account.
Foreign direct investment, borrowing from abroad, export earning from merchandise, export earnings from banking services, earning from tourism, foreign portfolio investment.

 Current Account Capital Account Export earnings from banking services Foreign direct investment Earning from tourism Borrowing from abroad Export earnings from merchandise Foreign portfolio investment

Question 3.
The open economy multiplier is smaller than that in a closed economy. Do you agree? Give reason.
Yes, I do agree with this statement.
The open economy multiplier is smaller than that in a closed economy because a part of domestic demand falls on foreign goods. An increase in autonomous demand thus leads to a smaller increase in output compared to a closed economy. It also results in a deterioration of the trade balance

Question 4.
Complete the following table.

• Export > Import
• Export = Import
• Export < Import

• Export > Import – Trade surplus
• Export = Import – Trade balance
• Export < Import – Trade deficit

Question 5.
Export promotion is one of the key factors for correcting disequilibrium in BOR Is there any other measure for correcting BOP? If yes, suggest 3 measures.
Measures to correct BOP disequilibrium,

• Increase in production
• Reduction in imports
• Encouraging foreign investment
• Promotion of exports

Question 6.
What is the MPM (Marginal propensity to import) When M = 60 + 0.67?
Marginal propensity to import (MPM) is the fraction of an additional currency of income spent on imports. The concept of MPM is same as the marginal propensity to consume (MPC). Thus, demand for imports is to depend on income and have an autonomous component.

Question 7.
Point out the items included in current account transactions of BOP.
The current account includes receipts and payments on account of:

1. export and import of goods and services
2. tourism services
3. foreign investment incomes and out payments
4. private transfer payments
5. inter-government transfer payments.

Question 8.
What is trade deficit? Calculate the trade deficit from the following data.

Trade deficit is the difference between export of goods and import of goods in trade in goods in current account. It is the situation where import is greater than export.
Export of goods = 90,660
Import of goods = 1,20,364 – 90,660 = 29,704 crores

Question 9.
a. Recently the government of UK decided to relax the visa norms to Indian visitors.
b. The government of India approved a purchase of weapon for Indian defence from rest of the world for an amount of 82000 crores

1. How does these decisions affect the demand for foreign exchange?
2. Analyse the consequences in the foreign exchange market with the help of a diagram.
(supply curve of foreign exchange remain the same)

1. Demand for foreign exchange increases

2. diagram

### Plus Two Economics Open Economy Macroeconomics Five Mark Questions and Answers

Question 1.

1. tea, coir, tourism
2. rice, banking services, insurance service, transport services
3. foreign direct investment, foreign portfolio investment, remittances, borrowings
4. foreign investment, remittances, export earning from goods, export earning from services

1. Tourism. Others are visibles
2. Rice. Others are invisibles
3. Remittances. Others are capital receipts
4. Remittances. Others are capital receipts.

Question 2.
Match the following.

 A B Bretton Woods system 1944 SDR 1967 Fixed Exchange Rate Pegged Rate Triffin Dilemma Dollar accumulation Flexible Exchange Rate Floating Rate

 A B Bretton Woods system Pegged Rate SDR Dollar accumulation Fixed Exchange Rate 1944 Triffin Dilemma Floating Rate Flexible Exchange Rate 1967

Question 3.
If c (marginal propensity to consume) = 0.8 and m (marginal propensity to import) = 0.3,

1. Find the open and closed economy multiplier
2. If domestic autonomous demand increases by 100, find the output level in a closed and an open economy.

1. Closed economy multiplier
$$=\frac{1}{1-c}=\frac{1}{1-0.8}=\frac{1}{0.2}=5$$
Open economy multiplier
$$=\frac{1}{0.5}=\frac{1}{1-0.8+0.3}=\frac{1}{1-0.5}=\frac{1}{0.5}=2$$

2. If domestic autonomous demand increases by 100, in a closed economy output increases by 500 whereas it increases by only 200 in an open economy.

Question 4.
Differentiate between fixed exchange rate and flexible exchange rate.
In a system of flexible exchange rates (also known as floating exchange rates), the exchange rate is determined by the forces of market demand and supply. Countries have had flexible exchange rate system ever since the breakdown of the Bretton Woods system in the early 1970s. Prior to that, most countries had fixed or what is called pegged exchange rate system, in which the exchange rate is pegged at a particular level.

Sometimes, a distinction is made between fixed and pegged exchange rates. Under a fixed exchange rate system, such as the gold standard, adjustment to BoP surpluses or deficits cannot be brought about through changes in the exchange rate.

Question 5.
What do you mean by managed floating? How far it is a mixture of fixed exchange rate and flexible exchange rates?
Without any formal international agreement, the world has moved on to what can be best described as a managed floating exchange rate system. It is a mixture of a flexible exchange rate system (the floating part) and a fixed rate system (the managed part).

Under this system, also called dirty floating, central banks intervene to buy and sell foreign currencies in an attempt to moderate exchange rate movements whenever they feel that such actions are appropriate. Official reserve transactions are, therefore, not equal to zero.

Question 6.
Distinguish between the nominal exchange rate and the real exchange rate. If you were to decide whether to buy domestic goods or foreign goods, which rate would be more relevant?
The price of one currency in terms of the other is known as the exchange rate. Nominal exchange rates are bilateral in the sense that they are exchange rates for one currency against another and they are nominal because they quote the exchange rate in money terms, i.e. so many rupees per dollar or per pound.

However, the real exchange rate is the ratio of foreign to domestic prices, measured in the same currency. It is defined as Real exchange rate = ePf/P where P and Pf are the price levels here and abroad, respectively, and e is the rupee price of foreign exchange (the nominal exchange rate).

The real exchange rate is often taken as a measure of a country’s international competitiveness. Therefore, real exchange rate is considered to be more relevant.

Question 7.
Balance of payment is a broader concept than balance of trade. Give explanation to this view.
Balance of trade is the record of a country’s visible export and visible imports. It includes only visible trade and excludes invisible trade of services. However, balance of payment is a more comprehensive term which denoted a country’s total monetary transactions with the rest of the world. It includes both visible and invisible trade of goods and, services.

The balance of payments (BoP) records the transactions in goods, services and assets between residents of a country with the rest of the world. There are two main accounts in the BoP the current account and the capital account.

Question 8.
The current account is differentiated from capital account. Do you agree? Give explanation.
Yes. The current account balance is the sum of the balance of merchandise trade, services and net transfers received from the rest of the world. The capital account balance is equal to capital flows from the rest of the world, minus capital flows to the rest of the world.

Question 9.
Illustrate the method of determining equilibrium under flexible exchange rate system. Also, show the effect of increase in demand for imports in the foreign exchange markets.
In a system of flexible exchange rates, the exchange rate is determined by the forces of market demand and supply. In this case of flexible exchange rates without central bank intervention, the exchange rate moves to clear the market, to equate the demand for and supply of foreign exchange. In the following figure equilibrium exchange rate is e* which is determined by the forces of demand and supply.

At the initial equilibrium exchange rate e*, suppose there is now an excess demand for foreign exchange. To clear the market, the exchange rate must rise to the equilibrium value e1 as shown in the following figure.

The rise in exchange rate (depreciation) will cause the quantity of import demand to fall since the rupee price of imported goods rises with the exchange rate. Also, the quantity of exports demanded will increase since the rise in the exchange rate makes exports. less expensive to foreigners. At the new equilibrium, the supply and demand for foreign exchange is again equal.

Question 10.
Differentiate between devaluation and depreciation.
Devaluation means increase in exchange rate. Devaluation is said to occur when the exchange rate is increased by social action under a pegged exchange rate system. Devaluation is used as a tool to bridge the gap of trade deficit.

On the other hand, change in the price of foreign exchange under flexible exchange rate, when it becomes cheaper as compared to domestic currency is known as depreciation.

Question 11.
Compare balance of trade (BOT) and balance of payments (BOP).
Balance of trade is the difference between money value of imports and exports of material goods only whereas BOP is the difference between a country’s receipts and payments in foreign exchange. The difference between the two can be summarized as follows:

 BOT BOP 1. It records only merch­andise transactions 1. It records transactions relating to both goods and services 2. It does not record trans­actions of special nature. 2. It records transactions of capital nature. 3. It is a narrow concept because it is only one part of BOP account 3. It is wider concept because it includes balance of trade, balance of Services, balance of unrequired transfers and balance of capital transactions. 4. It may be favorable, un favorable or equilibrium 4. It always remains in balance in accounting sense because receipt side is always made to be equal to payment side

Question 12.
Complete the following flow chart.

Question 13.
Distinguish between autonomous and accommodating transactions?
International economic transactions are called autonomous when transactions are made independently of the state of the BOP. These items are called above the line.

On the other hand, accommodating transactions are determined by the net consequences of the autonomous items, that is whether the BOP is in surplus or deficit. These items are called ‘below the line.

Question 14.
Suppose the equilibrium exchange rate is shown in the figure. What happens to this equilibrium situation when there is increase in demand for foreign exchange?

When the demand for foreign exchange increases, there is rise in exchange rate (depreciation). At the higher exchange rate, more quantity of foreign exchange will be transacted. This is shown below.

Question 15.
Distinguish between appreciation and depreciation. Identify what happens to the exchange rate of rupees in 2015 compared to 2014.

 Year Rupee dollar exchange rate 2014 50. 2015 60.

Appreciation refers to the increase the exchange rate of a currency. Depreciation refers to the decrease in the rate of exchange of currency. Both appreciation depreciation of exchange rate occurs due to the changes in the supply and demand of currencies. Compared to 2014 there is a depreciation of currency exchange rate in 2015.

Question 16.
The diagram below shows how the rate of exchange is determined in a free market.

Show the effect of the following on the exchange rate.

1. The rate of interest of the country increases.
2. The rate of inflation of the nearby countries.

1. When the rate of interest increases the rate of exchange will increase. This is because an increased rate of interest would attract more depositors into the country, the demand for the currency would increase and the rate of interest also will increase as shown in the diagram below.

2. When the inflation of the nearby countries increases the people around would prefer to buy goods from this country. So the demand for the currency would increase leading to an increase in the rate of exchange.

Question 17.
Exchange rate is determined through different methods. Diagrams related with exchange rate are given below.

1. Identify the Exchange rate system corresponding to each diagram
2. Distinguish between the two.

1. Diagram A is Flexible Exchange Rate System and Diagram B is Fixed Exchange Rate System

2. In a system of flexible exchange rates (also known as floating exchange rates), the exchange rate is determined by the forces of market demand and supply. Countries have had flexible exchange rate system ever since the breakdown of the Bretton Woods system in the early 1970s.

Prior to that, most countries had fixed or what is called pegged exchange rate system, in which the exchange rate is pegged at a particular level. Sometimes, a distinction is made between fixed and pegged exchange rates. Under a fixed exchange rate system, such as the gold standard, adjustment to BoP surpluses or deficits cannot be brought about through changes in the exchange rate.

### Plus Two Economics Open Economy Macroeconomics Eight Mark Questions and Answers

Question 1.
Determine the equilibrium level of income based on the following information.
C = 100 + 0.75 (Y – T)
I = 200 – 2000;
G = 100
T = 80 + 0.20Y
X = 50
M = 20 + 0.10Y

## Plus Two Chemistry Chapter Wise Questions and Answers Chapter 6 General Principle and Processes of Isolation of Elements

Students can Download Chapter 6 General Principle and Processes of Isolation of Elements Questions and Answers, Plus Two Chemistry Chapter Wise Questions and Answers helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

## Kerala Plus Two Chemistry Chapter Wise Questions and Answers Chapter 6 General Principle and Processes of Isolation of Elements

### Plus Two Chemistry General Principle and Processes of Isolation of Elements One Mark Questions and Answers

Question 1.
Siderite is chemically _______________.
Iron carbonate (Fe2CO3)

Question 2.
A mineral is called an ore if
(a) The metal present in the mineral is costly
(b) A metal can be extracted from it
(c) A metal can be profitably extracted from it
(d) A metal cannot be extracted from it.
(c) A metal can be profitably extracted from it

Question 3.
Predict whether the following statement is true or false? Calcination is done in presence of plenty of air.
false

Question 4.
The Ellingham diagram is a plot of
(a) ∆fG° vs T
(b) ∆fH° vs T
(c) ∆fS° vs T
(d) ∆fG° vs ∆f
(a) ∆fG° vs T

Question 5.
Which of the following metals can be refined using van Arkel method?
(a) Ni
(b) Si
(c) Cu
(d) Zr
(d) Zr

Question 6.
Arrange the five elements which together constitute more than 90% of earth’s crust in the decreasing order of their abundance.
Oxygen > Silicon > Aluminium > Iron > Calcium.

Question 7.
Suggest the method for the refining of following metals.

1. Copper
2. Germanium
3. Zirconium

1. Copper – Electrolytic refining
2. Germanium – Zone refining
3. Zirconium – van Arkel method

Question 8.
Which one of the following does not occurs as sulphide ore
(a) Zn
(b) Cr
(c) Ag
(d) Fe
(e) Hg
(b) Cr

Question 9.
Refining of zirconium is by __________________ method
Van Arkel method.

Question 10.
Sphalerite is concentrated by ___________.
Froth floation

Question 11.
Litharge is an ore of ___________.

Question 12.
The process used for the extraction of sodium is
Down’s process

### Plus Two Chemistry General Principle and Processes of Isolation of Elements Two Mark Questions and Answers

Question 1.
Explain the terms
Calcination and Roasting with example.

Question 2.
Complete the table:

 A B 1. Iron Haematite 2. Sodium ………………… 3. Chromium …………………. 4 …………….. SnO2 5 …………….. CuFeS2

 A B 1. Iron Haematite 2. Sodium Rock salt 3. Chromium Chromite ore 4. Tin SnO2 5. Copper CuFeS2

Question 3.
Why is the reduction of a metal oxide easier if the metal formed is in liquid state at the temperature of reduction?
The entropy is higher if the metal is in liquid state than in solid state. The value of (∆S) of the reduction process is +ve when the metal formed is in liquid state the metal oxide being reduced is in solid state. The value of ∆GΘ becomes more on -ve side and the reduction becomes easier.

Question 4.
Before final metallurgical operations the concentrated ore is subjected to some preliminary chemical treatments. Two processes employed for this purpose are carried out in reverberatory furnace.

1. Name the two processes.
2. To which form the ore is converted through these processes?

1. Calcination and Roasting
2. In both processes ore is converted into oxide form.

Question 5.
Match the following:

 Process Metal Purified 1) Mond’s Process Zirconium 2) van Arkel process Silicon 3) Zone refining Zinc 4) Distillation Nickel

 Process Metal Purified 1) Mond’s Process Nickel 2) van Arkel process Zirconium 3) Zone refining Silicon 4) Distillation Zinc

Question 6.
What is Ellingham diagram? Mention its application.
It is a graph showing the variation of ∆rG°forthe formation of oxides with temperature. It helps in the choice of reducing agent in the reduction of oxides.

Question 7.
Although thermodynamically feasible, in practice, magnesium metal is not used for the reduction of alumina in the metallurgy of Aluminium. Why?
The process would be uneconomic because Mg itself is a costly metal. Moreover, there is one technological difficulty also. The reaction between Mg and Al2O3 is exothermic. If the temperature increases to 2000 K then the reverse reaction becomes feasible, i.e., Al starts reducing MgO.

Question 8.
Distinguish between mineral and ore.

• Mineral: Various compounds of metals which are found in earth’s crust.
• Ores: The minerals from which metal can be easily and economically extracted.

Question 9.
Which flux can be used to remove a metal oxide impurity from a sulphide ore of noble metal? Substantiate.
Silica, SiO2. Generally, metal oxides are basic in nature. To remove basic impurities an acidic flux like SiO2 is used.

Question 10.
Match the following:

• Aluminium – Leaching – Bauxite
• Copper – Malachite – Brass
• Mond’s process – Nickel – CO

Question 11.
Match the following:

• Mond’s process – Vapour phase refining – Nickel
• Sulphide ore – Zinc blende – Froth floatation
• Germanium – Zone refining – Semiconductor
• Calamine – ZnCO3 – Calcination

Question 12.
Differentiate Cast Iron and pig iron.
1. Cast iron:

• It is a form of iron obtained from pig iron.
• lt has 3% carbon content.

2. Pig iron:

• It is the least pure form of iron obtained directly from the blast furnace.
• It contains about 4% carbon and many impurities in smaller amount.

Question 13.
How is leaching carried out in case of low grade copper ores?
Copper is leached out using acid or bacteria. The solution containing Cu2+ ions is treated with iron scrap or H2 to recover copper.
Cu2+(aq) + Fe(s) → Cu(s) + Fe2+(aq)
Cu2+(aq) + H2(g) → Cu(s) + 2H+(aq)

Question 14.
Why is the extraction of copper from pyrites more difficult than that from its oxide ore through reduction?
Carbon is a poor reducing agent for sulphide ores whereas it is good reducing agent for oxide ores.

Question 15.
What is the role of graphite rod in the electrometallurgy of aluminium?
Graphite rod acts as anode in the electrometallurgy of aluminium. Graphite anode facilitates reduction of Al2O3 to aluminium by electrolysis. Carbon reacts with oxygen liberated at anode producing CO and CO2

Question 16.
Name the common elements present in the anode mud in electrolytic refining of copper. Why are they so present?
The elements antimony, selenium, gold, silver, platinum, etc. are present in the anode mud during refining of copper. These impurities being less electropositive do not undergo oxidation at anode and hence settle down as such.

### Plus Two Chemistry General Principle and Processes of Isolation of Elements Three Mark Questions and Answers

Question 1.
The following are some ores. Calamine (ZnCO3), Haematite (Fe2O3), Cinnabar (HgS), Bauxite (Al2O3.2H2O)

1. Which ore is concentrated by froth floating process?
2. How is Haematite concentrated?
3. Which of the ores is concentrated by leaching?

1. Cinnabar (HgS). Sulphide ores are concentrated by this process.
2. By magnetic separation.
3. Bauxite (Al2O3.2H2O)

Question 2.
Some data are given below:
(Iron tank, Carbon lining, Cryolite, Carbon blocks, Electricity)

1. Identify the metal whose metallurgy is associated here.
2. Explain the extraction of this metal.

1. Aluminium.
2. The alumina is dissolved in a mixture of molten cryolite. It is then electrolysed in a rectangular steel tank, with carbon lining, which serves as cathode. Anode is a set of thick carbon rods suspended from top into the fused Al2O3. The temperature is maintained as 1200 Kand 1310 K. Oxygen is evolved at anode which reacts with carbon of anode producing CO and CO2. Aluminium formed at the cathode gets collected.

Question 3.

1. What is the role of cryolite in the metallurgy of aluminium?
2. Match the following :
 Metal Process 1. Al Mond’s process 2. Si van Arkel process 3. Zr Zone refining 4. Ni Leaching

1. Cryolite is used as a solvent to dissolve alumina.
2.

• Al → Leaching
• Si → Zone refining
• Zr → van Arkel process
• Ni → Mond’s process

Question 4.

1. Name the chief ores of Aluminium and Iron.
2. What methods are employed for the concentration of these ores?

1. The chief ores of Aluminium and Iron

• Al → Bauxite
• Iron → Haematite

2. Bauxite is concentrated by leaching and haematite is concentrated by magnetic separation.

Question 5.
The choice of reducing agents in a particular case depends on the thermodynamic factor.

1. How far do you agree with this statement?
2. Support your opinion with an example.

1. The statement is true. Choice of reducing agents depends strongly on factors like ΔH, ΔS, ΔG and T for the formation of the oxide to be reduced.
2. Electropositive metals like Al, K etc. can be extracted using electricity. Whereas CO is used for reducing haematite in the extraction of iron.

Question 6.
You are provided with samples of impure copper and germanium.

1. Which method would you recommend for the purification of each of these metals?
2. What is ‘‘Copper matte”? How is it formed?

1. Coper – Electrolytic refining
Germanium – Zone refining
2. The copper in the furnace that contains Cu2S and FeS is called copper matte. It is formed when copper ore is heated in reverberatory furnace after mixing with silica.

Question 7.
As a part of a field trip, students visited a metallurgical plant. They saw that metal is heated in a slopping floor of the furnace.

1. Give the name of this process.
2. Which type of metals are purified by this method?
3. Give example.

1. Liquation
2. Metals with low melting point

Question 8.
Blast furnace produces molten iron which contains impurities such as carbon and sulphur. To make steel, oxygen is blown into the surface of the molten iron. Other elements are then added to give the type of steel required.

1. What is slag?
2. Name the two gases formed when oxygen reacts with the impurities.
3. Name one element which is added to iron to make steel.

1. Slag is a substance formed by the reaction of impurities with flux.
2. Carbon dioxide and Sulphur dioxide.
3. Carbon.

Question 9.
What do you mean by refining? Mention the methods also.
The process of removal of impurities from the crude metal is called refining. The methods are:

• Distillation
• Liquation
• Electrolytic refining
• Zone refining
• Van Arkel process
• Mond’s process
• Chromatographic methods

Question 10.
Copper can be extracted by hydrometallurgy but not zinc. Explain.
Metals occupying low positions in the electrochemical series can be extracted by hydrometallurgy. The metals occupying higher positions in the electrochemical series cannot be extracted by hydrometallurgy because such metal ions are difficult to be reduced.

Copper can be extracted by hydrometallurgy because it occupies lower position in the electrochemical series but Zn occupies higher position.

### Plus Two Chemistry General Principle and Processes of Isolation of Elements Four Mark Questions and Answers

Question 1.
The metals such as Ge, Ga, Si etc. are used as semiconductors. So they are to be obtained at high degree of purity.

1. Name the method to obtain highly pure Si.
2. Ti is purified by using I2. Name the process.
3. What is Mond’s process?

1. Zone refining.
2. van Arkel Process.
3. For the refining of nickel. In this process, nickel is heated in a stream of CO forming a volatile complex, Ni(CO)4. It is decomposed at high temperature giving pure nickel.

Ni + 4CO → Ni(CO)4 → Ni + 4CO

Question 2.
Some ores are given below:
(ZnS, Al2O3, Fe2O3,Cu2S)
Make a table containing ores, methods of concentration, name of the metal and alloy of the metal.

Question 3.

1. The value of enthalpy of formation for Cr2O3 is -540 kJ/mol and that of Al2O3is -827 kJ/mol. Is the reduction of Cr2O3 possible with Al?
2. Name the metallurgical refining techniques used for Ge and Ni.

1. Yes. From the enthalpy of formation values of the concerned oxides it is celar that Al is a strong reducing agent than Cr.

2.

 Element Metallurgical technique Ge Zone refining Ni Mond’s process

Question 4.

1. What is the importance of Ellingham diagram?
2. Using the following Ellingham diagram select the suitable reducing agents that can be used for the reduction of Fe2O3 in blast furnace above and below 1000 K.

1. Ellingham diagram help us in predicting the feasibility of thermal reduction of ore. The criteria is that at a given temperature Gibbs energy of reaction should be negative.

2. Below 1000 K CO is the good reducing agent while above 1000 K carbon is the good reducing agent. This is because below 1000 K the (CO, CO2) line is below the (Fe, FeO) line. But, above 1000 Kthe (C, CO2) line is below the (Fe, FeO) line.

Question 5.
Bauxite is ore of Aluminium.

1. What do you mean by an ore?
2. Name the method which is used to purify Bauxite.
3. Write two examples for ores and their purification methods.

1. The mineral from which metal can be easily and economically extracted is called ore.
2. Leaching
3. Two examples for ores and their purification methods

• Hematite → Magnetic separation
• Cinnabar → Froath floatation

Question 6.

1. What is the role of depressant in froth floatation process?
2. Explain with an example.

1. Depressants prevent certain type of particles from forming froth during froth floatation process.
2. NaCN acts as a depressant for ZnS but not for PbS. Thus, when an ore containing PbS and ZnS is subjected to froth floatation process NaCN selectively prevents ZnS from coming to the froth but allows PbS to come with the froth. In this way, PbS can be separated from ZnS.

Question 7.

1. Which ore is used for the extraction of Al?
2. What do you mean by extraction of Aluminium?
3. Explain the process of purification of ore with chemical equations.

1. Bauxite
2. Removal of earthy impurities (gangue) from bauxite ore and separation of metallic aluminium is called extraction of aluminium.
3. Bauxite is treated with NaOH solution and sodium meta aluminate is formed. The aluminate solution is neutralised by passing CO2 gas and hydrated Al2O3 is precipitated by seeding with freshly prepared samples of hydrated Al2O3. Hydrated alumina is filtered, dried and heated to obtain pure Al2O3

### Plus Two Chemistry General Principle and Processes of Isolation of Elements NCERT Questions and Answers

Question 1.
Copper can be extracted by hydrometallurgy but not zinc. Explain.
Metals occupying low positions in the electrochemical series can be extracted by hydrometallurgy because the metal ions (Mn+) of such metals can be easily reduced by treatment with some more electropositive metal. The metals occupying higher positions in the electrochemical series cannot be extracted by hydrometallurgy because the metal ions of such metals are difficult to be reduced.

Copper can be extracted by hydrometallurgy because it occupies quite lower position in the electrochemical series. On the other hand, zinc cannot be extracted by hydrometallurgy because it occupies higher position in the series and has large negative reduction potential.

Question 2.
How is leaching carried out in case of low grade copper ores?
Copper is leached out using acid or bacteria. The solution containing Cu2+ ions is treated with iron scrap or H2 to recover copper.
Cu2+(aq) + Fe(s) → Cu(s) + Fe2+(aq)
Cu2+(aq) + H2(g) → Cu(s) + 2H+(aq)

Question 3.
Why is the extraction of copper from pyrites more difficult than that from its oxide ore through reduction?
Carbon is a poor reducing agent for sulphide ores whereas it is good reducing agent for oxide ores.

Question 4.
What is the role of graphite rod in the electrometallurgy of aluminium?
Graphite rod acts as anode in the electrometallurgy of aluminium. Graphite anode facilitates reduction of Al2O3 to aluminium by electrolysis. Carbon reacts with oxygen liberated at anode producing CO and CO2
At anode:
C (solid) + O2- (melt) → CO(g) + 2e
C(solid) + 2O2-(melt) → CO2(g) + 4e
At cathode:
Al3+(melt + 3e → Al(I)

Question 5.
Name the common elements present in the anode mud in electrolytic refining of copper. Why are they so present?
The elements antimony, selenium, gold, silver, platinum, etc. are present in the anode mud during refining of copper. These impurities being less electropositive do not undergo oxidation at the anode and hence settle down as such.

## Plus Two English Textbook Answers Unit 3 Chapter 2 Didi (Story)

Kerala State Board New Syllabus Plus Two English Textbook Answers Unit 3 Chapter 2 Didi Text Book Questions and Answers, Summary, Notes.

## Kerala Plus Two English Textbook Answers Unit 3 Chapter 2 Didi (Story)

Hsslive Plus Two English Textbook Answers are part of Kerala Plus Two English Textbook Answers Unit 3 Chapter 2 Didi

Question 1.
What was Shaheen’s first impression of orphanage?
In the orphanage she saw crying children, laughing children, quiet children and screaming children. She was confused. She saw the inequity of life there.

Question 2.
Why does she say that life was not perfect during summer vacation?
She says that life was not perfect during summer vacation because her summers were spent between the orphanage in Jakarta and trips back to Mumbai. In Mumbai she saw the extreme poverty and children begging forfood.

Question 3.
What was the ‘search’ Shaheen had in her childhood? How was India answering it?
The ‘search’ she had in her childhood was finding ways to help the kids in need. India was answering it because in India she found many children begging on the streets for food. She knew she could help them to live better lives.

Question 4.
What do you understand by the expression ‘manicured reality of my university life”?
‘Manicure’ means caring for the fingers and nails. Manicured reality is polished reality. As one who has studied in India, especially in the crowded Mumbai, the authorfelt her university life in the USA was manicured, highly polished.

Question 5.
On what conditions did Shaheen’s parents allow her to stay back in India?
They put forward two conditions: she would get admission into a good undergraduate college in the city and later she would go abroad for her graduate degree.

Question 6.
How did Shaheen get her admission to St. Xavier’s even when the admissions were closed.
I would say she forced the Principal to admit her. She entered the principal’s room through a side door. Before the surprised Principal, Fr. D’Cruz, could open his mouth she said to him, “Father, my life is in your hands. I want to do something for the children of India. I don’t know how, only that I must.” The Principal asked her a few questions and she was admitted.

Question 7.
What was the condition of Mumbai slums?
It was horrible. The slum once Shaheen walked into was a sprawling, low income community which was a maze of small alleyways. It was full of life. Some 10,000 people lived there without running water, no system of waste disposal, and shared six dark cubicle toilets in one alley.

Question 8.
How was Sandhya’s life different from that of Shaheen?
Sandhya’s life was utterly different from that of Shaheen. Like Shaheen she was also 18. Sandhya knew no English and Shaheen knew no Hindi. But Sandhya, wearing a sari, smiled, laughed and chatted a lot. Sandhya’s home was smaller than the bathroom of Shaheen’s house.

Question 9.
What is the basic principle ofAkanksha?
The basic principle of Akanksha is providing underprivileged children with opportunities for learning. Akanksha wants the classroom to be just a safe place for the children where they can forget, at least for some time, their roubles at home and study and also enjoy. Akanksha came into existence in 1991. It started with 15 children. Now it has 3500 children, with 58 centre and 6 schools. The children are taught, apart from English and Maths, values, self-esteem and confidence.

Question 10.
What did the volunteers teach at Akanksha?
At Akanksha the volunteers teach the underprivileged children basic English and Maths, and also values, self¬esteem and confidence.

Question 11.
What kind of difference, do you think, Akanksha must have brought in the slums?
Nowthe slum-dwellers knowthe importance of education. They also knowthe importance of hygiene and decent living. They have realized that they too can rise higher in the society with education, determination and hard work. Akanksha has provided people with hopes and dreams.

Think And Write

Question 1.
What kind of problems did Shaheen face when she settled in India?
She faced a lot of problems when she settled in India. She wanted to help the underprivileged people of slums, especially children. She wanted to teach them. But finding a place was difficult. She went to 20 schools asking them to give a room just for 3 hours in the morning to teach these poor children. All of them refused. Some thought the idea of teaching underprivileged children was too revolutionary. Some thought the children would spread diseases to other students. A principal of a reputed school even said that the glass bangles worn by the poor children would scratch the fine desks. Finally, when she was about to give up, the Principal of Holy Name High School in Colaba, agreed to give her a room. That was the first Akanksha centre.

Question 2.
What was the iniquity that she found in India?
She found a lot of iniquity in India. In a city like Mumbai where some of the world’s richest men live, there are also dirty slums where people live in conditions in which even animals would not live. One of the slums she visited was a sprawling, low income community which was a maze of small alleyways, full of life. Some .10,000 people lived there without running water, no system of waste disposal, and shared six dark cubicle toilets in one alley. She says the house of Sandhya was smaller than her bathroom! This is iniquity indeed.

Question 3.
Why, do you think, the principals of different schools refused to give a space for the children from the slum?
Shaheen says that the principals often gave illogical and even silly reasons for not giving a space for the children from the slum. Some thought the idea of teaching underprivileged children was too revolutionary. Some thought the children would spread diseases to other students. A principal of a reputed school even said that the glass bangles worn by the poor children would scratch the fine desks in the classroom!

Question 4.
Shaheen refers to Indian education system as ‘bookish’. Comment on this.
Shaheen is very right in saying that the Indian education system is bookish. We lay stress on book¬learning. We give a lot importance to studying things by heart. The examinations also check our memory and not our competence in doing things. Theory is given much more importance than practice. We may know a lot about America and England but may not know the things in our immediate locality.

Activity I (Job application/Resume)

Question 1.
(i) Study the poster.

It tells us about another initiative called “Teach for India” by Shaheen Mistri. It is an advertisement seeking volunteers to teach the children in low-income areas.

If you were to apply for this vacancy, what would you write in your application in the resume?
(i) Cover Letter
Joe Paul
Irinjalakuda North PO
PIN 680 125
15 June 2015

The Chairperson
Teach for India
Kalian Mumbai

Dear Sir,
I have seen your poster asking for people to work in your Enterprise. I would be glad to offer my services as a teacher at the secondary level.

I have a Master’s Degree in English from Ravishanker University, Raipur. I have worked as a teacher in HSS Irinjalakuda for 10 years, teaching English. I would like to utilize my talents forthe betterment of the underprivileged.

I shall be pleased if my application is given due consideration. Although I am willing to come at anytime, anywhere, for an interview I would prefer any day between 20 June and 20 July, preferably in the Thrissur district, of Kerala.

I had been dreaming of helping my countrymen in my own way and I look forward to this opportunity.

Thanking you cordially,
Yours faithfully
(Joe Paul)

(ii) RESUME OF JOE PAUL
Objective : To work in an Organization that works for the welfare of the underivileged

Experience:

• Teacher (HSS lnnjalakuda Teacher -1998-2008)
• Lecturer in English (Students PG Centre lnnjalakuda 2009-1015)

Activities: I am a member of the Rotary Club, irinjalakuda Branch. I have organized blood-donation campaigns.
Achievements: I have published many journal articles on the teaching of English.
Skills: Conversant with computer, Word. I have been the Volley-ball captain while at College. I play the guitar.
Languages: Malayalam, Hindi, English Interests: Reading, travel, Western music Joe Paul

Activity II (Job Interview:)

Question 2.
Suppose your application Is considered positively and you are invited for an interview. What kind of responses would you make for the following interview questions. Use formal and language and be honest In your answers.
Interviewer : Why do you prefer to teach?
You : I preférto teach because I believe it is the noblest profession. You mould minds.
Interviewer : Do you have any teaching experience?
You : Yes, I have. I have been teaching since 1997, when I completed my M.A. in English Literature.
I: What do you think is the most serious problem with the education in rural areas?
Y: The rural people, generally, have not understood the importance of education. When a boy or girl is big enough the parents expect the child to help them in the farm or in the household work. Many of them think sending children to school is a waste, especially sending girls to school.
I: If you were to change something about the current education system, what would that be?
Y: I would like to make learning less bookish. We emphasize on learning things by heart. Often in our examination we test memory. This should change. Education should be more practical.
I: How do you plan to create an impact in the society?
Y: I will do my best to teach the underprivileged so that they too can have opportunities like those bom with a silver spoon in their mouth. I will encourage the villagers to send their children to school without making them stay at home to help with the farming and other rural activities.

Activity III: (Modal Auxiliaries)

Read the notes on p. 114 and study the various verbs given in the table there, with their meanings. Read the examples and team howto use them.

LET’S PRACTICE

Question 2.
Given below is the vision of “Teach for India” as given in their website. Go through it and fill in the blanks in the passage with appropriate modal auxiliaries.
At Teach For India, each one of us feels lucky. We understand that it is just a matter of chance that we are where we are today. We didn’t choose the family that we were bom into, or choose the fact that our parents could afford.to give us quality education. Every time we make a choice, we feel lucky. However we cannot help but think what if these choices were not available to us?

It is this thought that makes us work towards that one day when every child in India would attain an excellent education. The family or the demographics that a child is bom into might not determine his or her destiny. We understand the importance of education but more importantly, we understand the value of each those 320 million lives andthe potential in every one of them. That’s what we are working towards – A day when every child gets the opportunity to attain an excellent education. A day when we could empower every human being with choice. Because that’s what every child deserves.

Activity IV (Role Play)

(Read the instractions on page 115)
(A conversation between Shaheen and her mother)
Shaheen: Good morning, mummy. How are you today?
Mother: Good morning, Shaheen. I am fine. What about you? You sound very excited.
S : I’m excited mummy. I have a plan.
M : A plan? What plan?
S : Mummy, I don’t want to go back to the USA at this time. I want to stay in India.
M : What? You want to stay in India? Have you gone crazy?
S : Mummy, I have not gone crazy. I want to do some service to the underprivileged children here.
M : Forget about service. You go to the Sates to continue with your studies.
S : My mind won’t let me go mummy. I am begging you to allow me to stay here.
M : Father will be so angry with you. You know how hot-tempered he is.
S : I will persuade him. I know he has a warm heart inside. You recommend my case to him.
M : I will do on two conditions: First you get admission in a good college in Mumbai. After you get yourdegree, promise that you will go abroad for higher studies.
S : I accept the conditions.
M : Let me warn you. Staying in India permanently is not like visiting it on vacation.
S: I know mummy. I have seen enough of Mumbai to understand that.
M : I am not too happy with your decision. But what to do? You’re our only daughter and we can’t refuse your request.
S: Thank you mummy. Thank you very much. I promise you I will make you proud.
M: Okay. Take care! And remember your promises!

Activity V (Project)

Action Plan

Name of the School: St. Joseph’s HSS, Kattoor Problem Identified: Water shortage during summer Reasons: There is no well in the compound. The school depends on the pipe-borne water supplied by the Municipality.
Plan Date: 15 June 2015
Completion Date: 15 September 2015

Possible challenges/difficulties:
I) The terrain is dry and so finding water in a well might be difficult. In that case a deep bore-well has to be planned. It might prove very expensive.
II) Participation by the Municipality might be minimal.
III) The community might not show sufficient interest in making contributions.

Activity VI: (Let’s Edit)

A website called studentjob is offering internship jobs for students.

Question 3.
Here is an application letter that a student has drafted to apply for the post of a marketing intern. Read it carefully and correct the mistakes in it Also rewrite the letter after corrections.
Dear Sir,
I would like to apply for the position of a Marketing Intern, as advertised in studentjob.co.in. I am a II Year student, doing M.Com. at the University of Calicut. My specialization is in Marketing.

I have always had a keen interest in marketing and that influenced my decision to study Marketing at the university and take part in extra-curricular activities. I am an active member of the Marketing Society where I help arranging events, society meetings and talks from prospective employers. I was responsible for establishing an effective marketing campaign for the launch of a new bookstore in the campus, using various methods such as social media. I therefore have a strong understanding of how modern-day marketing techniques can be used for business opportunities and networking.

Furthermore, I have been elected as the Team Leader of ‘Student Enterprise’, where we are required to develop our own business idea and pitch it to potential investors against an opposing team. This allows me to develop my leadership skills by delegating the appropriate roles and responsibilities to each team member, ensuring the team will successfully reach its aims and objectives.

I have many skills which I am able to contribute to the job role. My excellent communication skills allow me to interact with members of an organization at all levels. I developed my public speaking and presentation skills by making university presentations to new and prospective students and to the members of my Faculty. I am organized, efficient and strive to take up any challenge given to me to the highest standard.

Attached is a copy of my CV. I can provide the names of referees who will support my application.

I look forward to hearing from you.

Yours faithfully,
Priya Sekhar

Question 1.
‘We can complain because rose bushes have thorns or rejoice because thorn bushes have rose.’ – Abraham Lincoln.

Question 2.
Here perspectives make a difference. Read the experience the poetic rendition of Stammer by K. Satchidanandan.

### Didi (Story) Edumate Questions and Answers

Question 1.
Read the following extract from the lesson ‘Didi’ and answer the questions that follow.
“On one blistering Mumbai day my taxi stopped at a traffic signal. Three children ran upto my window, smiling and begging and at that: moment, I had a flash of introspection”.
a) Who is the speaker?
b) The word introspection’ here means
c) How does the author look at the meaning of life?
a) Shaheen Mistry
b) self-examination
c) She looks at the meaning of life with some concern. She is moving in a taxi and when it stops at a traffic signal three children come begging. They were smiling. The author must have wondered how these children could smile even in such precarious circumstances. They are zigzagging through the Mumbai traffic and any moment they can be hit by a moving vehicle. And look at the poverty of these children! They should be going to school and playing around with their mates at this age. But they are begging for their livelihood. This is the Mumbai of millionaires!

Question 2.
You happen to see the following advertisement and got interested and decided to apply for the same. Prepare an application and resume.
Vacancy Announcement
A reputed manpower company invites applications forthe following posts. .
No.1: Manager
Qualification: Should be a graduate in Commerce, experience in manpower field, good communication skill in English, age above 30 years.
Apply with Resume within 7 days: info@samintl.co.in
Only short listed candidates will be called for interview.
info@saminl.co.in

Dear Sirs,
Sub: Application forthe post of Manager.

I saw your advertisement. I am interested in applying for the post as I thought my qualification and experience would suit your requirements.

I am enclosing my detailed resume for your perusal.

I will be available for an interview from now till the end of this month. You may decide the time and place. I will present all the original documents at the time of the interview.

Hoping to get the interview letter soon,

Yours faithfully,
Hamza Mohammed

Resume of Hamza Mohammed
Objective: To work in a company which can utilize my services and, at the same time, enable me to sharpen my capabilities forthe betterment of all.

 Name & Address: Hamza Mohhammed XV/56 M.G. Road, Kochi Mobile Phone : 864702828888 e-mail: hamzamohd@hotmail.com Age and date of birth: 32 years, 11 January 1985 Nationality: Indian Marital status: Single Educational Qualifications: i) M.Com. with 76% marks, Calicut University, 2008 ii) B.Com. with 82% marks, Calicut University 2006 iii) +2 with all A’s from Don Bosco HSS Irinjalakuda. 2003 Technical Qualifications: Diploma in Computer Programming with specialization in Java, SQL and C++. Experience: I have been working as the Manager of GJ Info tech, Palarivattom Kochi, since July 2010. Special Abilities: Creating new computer programmes according to specifications. I have Leadership qualities. Hobbies: Travel and reading Languages known: Malayalam, English and Hindi Referees: 1. Prof. Naveen Vithayathil Khanna Nagar, Koratty, Chalakudy 2. Mr. Tom Nettikadan M.L.A., Chalakudy

Question 3.
While appearing for the Plus one improvement examination 2016, you forgotto fill in certain entries in the main answer sheet. Hence your result is withheld by the Directorate of Higher Secondary Education. When you contacted the office concerned you were informed to send an e-mail citing your points. Now draft the e-mail.
higheredudirectorate@hotmail.com

Sir,
I wrote the Plus One Improvement Examination 2016. But my result is withheld. When I contacted your office I was told thaf my exam number was not clearly visible in my History Paper and that is why the result was withheld. I am sorry forthe mistake. Here is my exam number: HSS 45678123. My Centre was Don Bosco HSS, irinjalakuda, Thrissur District.

Kindly take necessary action and publish my result.

Thank you,
Jones Mathew

Question4.
Given below are some findings of the research carried out by Delhi Diabetes Research Center on the changing food habits among children. Study them carefully and write an article for your school magazine.

(Hints: 85% school children-diabetic patients- Western eating styles-consumes fast food frequently- 62% eat junk food-green vegetables avoided-25% do not exercise-one in four children obese-prone to develop adult diseases-heart attack, diabetics-memory loss etc.)
Changing Food Habits among Children The Delhi Diabetes Research Centre carried out a research for finding out the changing food habits among children. Its findings should cause us some concern in this regard.

The researchers found that 85% of the school going children have some form of diabetes. This is very alarming statistics. This has happened mainly because we have blindly copied the Western eating habits. The climate in the countries in the West is generally very cold. Their food habits suit that climate. But here in India we are in the tropics and the weather is not all that cold. Still we eat what the Westerners eat. Our children consume a lot of fast food – pizza, burghers, KFC (Kentucky Fried Chicken) and so on. It is surprising that 62% of the children eat junk food. Our children studiously avoid green vegetables from their diet. It is surprising that 25% o the children do not get any exercise.

They go to school in the school bus, come home, sit down to do their home work and then they spend their time before the TV or their computers playing various games. The result is terrible. One in four children is obese – overweight. The obese children are likely to develop adult diseases like heart attack, severe diabetics and memory loss. There have been instances of teenagers dying of heart attack. This is something unheard of in the past. Many children suffer from serious diabetics. Children fail in exams because they have lost their memory power because of the junk food they are consuming.

Parents, who are so much concerned about the welfare and future of their children, should stop giving them junk food. Children should be made aware of the risks involved in eating too much of fast foods. The food may be tasty but it can kill them fast!

Question 5.
With the idea of teaching the underprivileged children, Shaheen Mistry decided to start Akansha Centre and the Principal of Holy Name School at Coloba agreed to give a room in his school. Write the likely conversation between Shaheen Mistry and the Principal. (At least four exchanges.)
Shaheen Mistry: Good morning, Sir! I am Shaheen Mistry, a social activist.
Principal : Good morning, Shaheen. I’ve heard aboufyou. What can I do for you?
SM : Sir, I think you can be of great help to me in solving a serious problem that we are facing. For educating the underprivileged children, we have started an organization called Akanksha. We want a room here for conducting our classes.
P : A room in this school? I don’t think it would be possible. We’re already running short of rooms and we find it hard to accommodate our own students.
SM : Sir, we need the room only after your regular class hours. We understand that you close the school at 4.00. So, maybe, from 4.30 you can lend us a room till 7.30 or so. Thus we get three hours to teach.
P : Shaheen, I am really sorry that I can’t do that. Soon after the class hours we get the rooms cleaned and keep them locked till the following morning.
SM : Sir, we assure you that the room you give us will be cleaned properly after our lessons are over. We are trying to uplift the underprivileged children.
P : I do want to help, but
SM : Sir, don’t say “but”.. Please give us a room. Your good gesture will help thousands of underprivileged children here. So, please be positive, Sir!
P : Okay, since you insist and since it is for a good cause, I will give you a room.
SM : Thank you, Sir! Thank you very much!
P : It’s okay.

Question 6.
The following is a conversation between the office assistant of a school and the book seller. Now complete the conversation choosing modal auxiliaries from the box given below, will, can, won’t, shall, needn’t, could
Bookseller : Excuse me sir. (a) ………… I meet the Principal right now?
Office Assistant: Sorry sir, he is attending a meeting.
Bookseller : Then if you don’t mind, you hand over this packet of books to the Principal, I shall be waiting outside.
Office Staff : Certainly sir, but you (b) ………… wait outside. He (c) ………… get enough time to see you and discuss the matter.
Book seller : OK sir, dont worry. I (d) ………… make a call and talk to the Principal.
Office Assistant: All right, bye.
a) Can,
b) needn’t,
c) won’t,
d) shall

– Shaheen Mistri

Shaheen Mistri is an Indian social activist and educator. She is the founder of Akanksha Foundation. She is also the CEO of Teach For India since 2008.

She was born in Mumbai in a Parsi family. Her father is a banker with Citigroup. After attending boarding school in Connecticut, USA, she moved to India for higher education. She got B.A. in Sociology. Later she got a Masters in Education from the University of Manchester.

### Didi (Story) Summary in English

“I reached to touch a rainbow today,
I reached up high so high.
And yet as high as I reached up,
I could not touch the sky.
I’ll reach to touch a rainbow again,
I’ll reach up higher than high,
And if I reach up high enough,
I just may skim the sky.”

Page 107: I remember sitting on the wide veranda of our Indonesian home, writing little poems and notes in a diary. I would sit and watch little ants carry large loads, determined to get to their destination. What was my destiny? I was 12. What had I achieved?

It was in 1983. We lived in Jakarta, in a lovely home on a quiet street. It was a pleasant life, until I was taken to visit an orphanage in the city. I don’t remember how the orphanage looked, but I vividly remember the children.

I saw different kinds of children-crying, laughing, quiet, screaming children. I did not know what to do. I returned to the orphanage every weekend. Perhaps it was curiosity or a sense of thankfulness for all that I had, or maybe a child’s desire to learn more about the world.

My father was a banker. He had to move from city to city.
I had to study in 10 schools in five countries and followed French, British, American and International school systems.

Page 107: I began to understand that life was not perfect during my summer vacations. My summers were spent between the orphanage in Jakarta and trips back to Mumbai. In Mumbai I volunteered at The Happy Home and School for the Blind. I remember thinking of the beauty you can create when you look beyond what you can see. The school had confident children running up and down the staircases or playing cricket on the terrace with a ball that jingled.

It was through these summer experiences in India that I began to see inequity. I’d go from a family lunch to the dining hall of the blind school. I would watch through the window of my air-conditioned car children begging in the streets. I saw piles of wasted food at a friend’s party. When I left I saw woman, sitting on the side of the road, giving out very small amount of dal and rice to her family members. I saw the slums of Mumbai. They appeared to be everywhere. I saw the disparity in the lives of people.

In 1989 I was on my vacation in India. On one hot Mumbai day, my taxi stopped at a traffic signal. Three children ran up to my window, smiling and begging. My mind started thinking. I suddenly knew that my life would have more meaning if I stayed in India.

In the days that followed I went on thinking about those kids. I realized the purpose of my life. I wanted to be part of making things better for children. I knew this could be my country. Whatever I did here could make more difference than my university life in America.

A week before I was to return to Boston, I telephoned my parents. I explained to them my desire to move back to Mumbai. They listened carefully. They advised me living in Mumbai would be greatly different from spending a vacation. But I persisted. They agreed on two conditions: I would get admission into a good undergraduate college in the city and later would go abroad for my graduate degree.

Page 109: My parents had studied at St. Xavier’s and so I wanted to study there. I wanted an appointment with the Principal. The office told me that admissions were closed three months earlier and the Principal does not give appointments. I was frustrated. A student had seen me talking with the Principal’s assistant. He told me that there was a side door to the Principal’s office and I could try it.

I went through the side door. The Principal, Fr. D’Cruz was surprised and before he could open his mouth I told him, “Father, my life is in your hands. I want to do something for the children of India. I don’t know-how, only that I must.” He asked me a few questions and I was admitted.

The academic system at St. Xavier’s was different from that of the US. Here bookish learning was stressed. I quickly realized that I would learn more in the city than in the classroom.

Now since I was in India, I wanted to understand it in a different and deeper way. I walked around the city. Once I walked into a sprawling, low-income community which was a maze of small alleyways, full of life. Some 10,000 people lived there without running water, no system of waste disposal, and shared six dark cubicle toilets in one alley.

Page 110:1 walked around that afternoon talking with children wondering how life would be different if each one of them had access to the opportunities to grow to their potential. As I was walking, a soft-spoken girl, in a sari, welcomed me into her home. Her name was Sandhya. She was 18, like me. She knew no English and I knew no Hindi. But she smiled, laughed and chatted a lot. I felt an immediate connection with her. Her life was so different from mine.

Every day I went to her house after college. Her home was smaller than the bathroom of our house. When children poked their heads inside the doorway to say ‘Hi’ to us, she would ask them to come in. These children formed the first class I would teach. Each day a few more children would come trying to learn a few words in English, ora little Maths ora song. I felt useful and confident.

This became my routine. I’d leave college and rush to my new world in the community. Here I saw truth and hope. The children shouted ‘Didi, Didi’when I went there. It was becoming a lifelong commitment.

‘Akanksha’ was bom of the simple idea that India had people who could teach. It had spaces that could be used as classrooms. It had funds to educate all the children. Everything was there. I simply had to bring them together.

The people in the community wanted only 3 things – housing, water and education. I knew that for the children to take education seriously, they have to be free from the community’s distractions. We started looking for our first Akanksha centre space.

I approached 20 schools in the city to give us one classroom in their building just for 3 hours every morning. All of them refused. Some thought the idea of teaching underprivileged children was too revolutionary. Some thought the children would spread diseases to other students. A principal of a reputed school even said that the glass bangles worn by the poor children would scratch the desks. Finally, when I was about to give up, the principal of Holy Name High School in Colaba, agreed to give me a room. That was the first Akanksha centre.

Page 111:1 mobilized volunteers from St. Xavier’s to teach. I made a rough plan of what they would teach. I wanted the classroom to be just a safe place for the children where they can forget, at least for some time, their roubles at home.

Akanksha came into existence in 1991. It started with 15 children. Now it has 3500 children, with 58 centre and 6 schools. The main things taught are English and Maths. Students are also trained in values, self-esteem and confidence.

(Excerpt from “Redrawing India” by Shaheen Mistri & Kovid Gupta)

### Didi (Story) Summary in Malayalam

Didi (Story) Glossary

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