Plus One

Kerala Plus One Maths Model Question Paper 2

Time Allowed: 2 1/2 hours
Cool off time: 15 Minutes
Maximum Marks: 80

General Instructions to Candidates :

• There is a ‘cool off time’ of 15 minutes in addition to the writing time .
• Use the ‘cool off time’ to get familiar with the questions and to plan your answers.
• Read instructions carefully .
• Read questions carefully before you answering.
• Calculations, figures and graphs should be shown in the answer sheet itself.
• Malayalam version of the questions is also provided.
• .Give equations wherever necessary.
• Electronic devices except non programmable calculators are not allowed in the Examination Hall.

Answer any six from question numbers 1 to 7. Each carries three scores.

Question 1.
Find 7+ 77 + 777 + 7777 +…. to n terms.

Question 2.

Question 3.
a. If A and B are two events in a random experiment, then
P(A) + P(B) – P(A ∩ B)
b. Given P(A) = 0.5, P(B) = 0.6 and P
(A ∩ B) = 0.3. Find P( A ∪ B) and P(A’).

Question 4.
Let A = {x:x is an integer, 1/2 < x < 7/2}
B = {2, 3, 4}
a. Write A in the roster form.
b. Find the power set of (A ∪ B)
c. Verify that (A – B )∪ (A ∩ B)=A

Question 5.
(i) Find the value of sin
\(\left( \frac { 3l\pi }{ 3 } \right) \)
(ii) Find the principal and general solutions of the equation cosx =
\(\frac { -\sqrt { 3 } }{ 2 } \)

Question 6.
A committee of 3 persons is to be constituted from a group of 2 men and 3 women.
a. In how many ways can this be done?
b. How many of these committees would consist of 1 man and 2 women.

Question 7.
a. Which one of the following points lies in the sixth octant?
i. (-4, 2, -5)
ii. (-4, -2, -5)
iii. (4, -2, -5)
iv. (4, 2, 5)
b. Find the ratio in which the YZ plane divides the line segment formed by joining the points (-2, 4, 7) and (3, -5, 8).

Answer any six from question numbers 8 to 17. Each carries four scores.

Question 8.
Consider the following statement :

a. Prove that P(1) is true.
b. Hence by using the principle of mathematical induction, prove that P(n) is true for all natural numbers n.

Question 9.
a. Write the negation of the statement: “Every natural number is greater than zero”
b. Verify by the method of contradiction : “P : √13 is irrational”

Question 10.
a. The 8th term in the expansion of (√2+√3)
is
i. 27 √2
ii. 27 √3
iii. 72 √2
iv. 72 √3
b. Find the term independent of x in the expansion of

Question 11.
a. In a random experiment, 6 coins are tossed simultaneously. Write the number of sample points in the sample space.

b. Given that P(A’)=0.5. P(B) = 0.6, P
(A ∩ B) = 0.3. Find P(A’) , P(A ∪ B), P(A ∩ B)and P(A ∪ B).

Question 12.
Let U={1,2, 3, 4, 5, 6, 7, 8, 9}, A= {1, 2, 4, 7} and B = {1, 3, 5, 7}
a. Find A ∪ B.
b. Find A’, B’ and hence show that (A ∪B)’ = (A’∩ B’)
c. The power set P(A ∪ B) has elements.

Question 13.
a. Let A= {7, 8} and B = {5, 4, 2} Find A x B.
b. Determine the domain and range of the
relation R defined by R = {(x, y): y = x + 1, x ∈ {0, 1,2, 3,4, 5}}

Question 14.
a. Find the distance between the points (2,-1, 3) and (-2, 1, 3)
b. Find the co-ordinates of the point which divides the line segment joining the points
(-2, 3, 5) and (1, -4,6) internally in the ratio of 2:3.

Question 15. A hyperbola whose transverse axis is X – axis, center (0,0) and the foci (±√10,0) passes through the point (3, 2)
a. Find the equation of the hyperbola.
b. Find its eccentricity.

Question 16.
a. Solve for the natural number n;
12. ⁽ⁿ⁺¹⁾ p₃ =5. ⁽ⁿ⁺¹⁾ p₃
b. In how many ways can 7 athletes be chosen out of 12?

Question 17.
Consider the statement: “n(n +1) (2n + 1) is divisible by 6”
a. Verify the statement for n = 2.
b. By assuming that P(k) is true for a natural number k, verify that P(k + 1) is true.

Answer any five from question numbers 18 to 24. Each carries six scores.

Question 18.
a. Match the following:

b. Find the derivatives of tan x using the first principles.

Question 19.
a. Find the equation of the line passing through the points (3, -2) and (-1,4).
b. Reduce the equation √3x + y – 8 = 0 into normal form.
c. If the angle between two lines is π/4 and slope of the line is 1/2, find the slope of the other line.

Question 20.
a. If x is the mean and c is the standard deviation of a distribution, then the coefficient of variation is……..

b. Find the standard deviation for the following data:
x_i : 3   8    13    18    23
f_i :  7   10  15    10    6

Question 21.
a. Which one of the following pair of a. Which one of the following pair of straight lines are parallel?
i. x – 2xy-4 = 0; 2x – 3y – 4 = 0
ii. x – 2y – 4 = 0; x – 2y – 5 = 0
iii. 2x – 3y – 8=0; 3x – 3y – 8 = 0
iv. 2x – 3y – 8 = 0; 3x – 2y – 8 = 0
b. Equation of a straight line is 3x – 4y + 10 = 0.Convert it into the intercept form and write the x-intercept and y-intercept.
c. Find the equation of the line perpen dicular to the line x – 7y + 5 = 0 and having x-intercept 3.

Question 22.
a. If (x+1, y-2) = (3,1), write the values of x and y.
b. Let A={ 1, 2, 3, 4, 5} and B={4, 6, 9} be two sets. Define a relation R from A to B by R={(x, y): x-y is a positive integer}. Find A X B and hence write R in the Roster form.
c. Define the modulus function. What is its domain? Draw a rough sketch.

Question 23.
a. Which among the following is the interval corresponding to the inequality -2 < x ≤ 3 ?
i. [-2, 3]
ii. [-2, 3)
iii. (-2, 3]
iv. (-2, 3)
b. Solve the following inequalities graphically
2x + y ≥ 4
x + y ≤ 3
2x – 3y ≤ 6

Question 24.
a. In how many ways can the letters of the word, PERMUTATIONS be arranged if:
i. the words start with P and end with S?
ii. there are always 4 letters between P and S?
b. In how many ways can 5 girls and 3 boys be seated in a row so that no two boys are together.
c. How many chords can be drawn through 21 points?

Answers

Answer 1.

Answer 2.

Answer 3.
a. P(A) + P(B) – P (A ∩ B) = P (A ∪ B)
b. P(A ∪ B) = P(A) + P(B) – P (A ∩ B)
= 0.5+ 0.6=0.3 = 1.1-0.3 = 0.8
P(A)’= 1- P (A) = 1-0.5 = 0.5

Answer 4.
a. Let A = {1, 2,3}
b. A ∪ B = {1, 2, 3,4}
P(A ∪ B)= {1}, {2}, {3}, {4},
{1, 2}, {1, 3}, {1, 4}, {2, 3},
{2, 4}, {3, 4}, {1, 2 ,3}, {1, 2, 4},
{2, 3,4}, {1,3,4}, {1,2, 3, 4},
{(j)} = 24 = 16 elements
c. A-B= {l}, A ∩ B = {2, 3}
(A – B) ∪ (A ∩ B) = {1, 2, 3} = A

Answer 5.

Answer 6.
a. Required number of ways = 5C₃ = 10
b. Number of committees =
2C₁ x 3C₂ = 2 x 3 = 6

Answer 7.
a. i. (-4, 2,-5)
b. Let YZ plane divides the line joining the points A (-2, 4, 7) and B (3, -5, 8) at R (x, y, z) in the ratio k: 1.
Then x coordinates of R = 0.

Answer 8.

Answer 9.
a. Let p : “Every natural number is greater than zero”. ~p: “ Every natural number is not greater than zero”.
b. Let us assume that √13 is a rational number.√13=a/b, where a and b are co-pnme, i.e., a and b have no common factors, which implies that 13b²= a² ⇒ 13 divides a. There exists an integer ‘k’ such that a= 13k a²= 169 k² ⇒ 13b²= 169k^{2 ⇒} 13k² ⇒ 13 divides b.
i.e., 13 dvides both a and b, which is contradiction to our assumption that a and b have no common factor. ∴ Our supposition is wrong. ∴ √13 is an irrational number.

Answer 10.

Answer 11.
a. 2⁶
b. P(A) = 0.5; P(B) = 0.6; P(A ∩ B) = 0.3
P(A’ ) = 1 – P(A) = 1 – 0.5 = 0.5
P(A ∪ B)=P(A)+P(B)-P(A ∩ B)
= 0.5 + 0.6 – 0.3 = 0.8
P( A ∩ B)=l-P P(A ∪ B)= 1-0.8 = 0.2
P(A ∪ B)=l-P(A ∩ B)= 1-0.3 =0.7

Answer 12.
U = {1,2, 3, 4, 5,7},
A = {1,2, 4, 7} and B = {1,3, 5, 7}
a. A ∪ B = {1,2, 3, 4, 5, 7}
b. A’ = {3, 5, 6, 8, 9}
B’ = {2, 4, 6, 8, 9}
A ∪ B = {1,2, 3, 4, 5, 7}
(A ∪ B)’ = {6, 8, 9}
A’∩ B’ = {6, 8, 9},
So (A ∪ B)’ = A’∩B’
c. The power set P(A ∪B) has 26 or 64 elements.

Answer 13.
a. A = {7, 8} and B = {5, 4, 2}
A x B = {(7, 5), (7, 4), (7,2), (8, 5), (8, 4), (8, 2)}
b. Domain = {0,1, 2, 3, 4, 5}
Range = {1,2, 3, 4, 5, 6}
R = {(0,1). (1, 2), (2, 3), (3, 4),(4, 5), (5, 6)}

Answer 14.

Answer 15.
Equation of hyperbola is

Answer 16.

Answer 17.
a. When n = 2,
2 (2+1) (2×2 + 1) = 2 x 3 x 5 = 30 is divisible by 6
b. P(k) = k(k + l)(2k + 1) is divisible by 6
P (k + 1) = (k + l)(k + 2) (2k + 1)
+ (k + 1) (k + 2)2 = (k + 1) (2k +1) k + (k + 1)
(2k + 1) x 2 + (k + 1) (k + 2)
= k (k + 1) (2k + 1) + 2 (k + 1)
[2k + 1 + k + 2]
= k (k + 1) (2k + 1) + 6(k + 1)²
is divisible by 6
∴ P(k + 1) is true

Answer 18.

Answer 19.

Answer 20.

Answer 21.
a. ii. x-2y-4 = 0; x-2y – 5 = 0
b. 3x – 4y + 10 = 0; 3x – 4y = -10

c. Slope of the given line is
\(\frac { -A }{ B } =-\frac { 1 }{ -7 } =\frac { 1 }{ 7 } \)
Slope of the required line is -7
Given x intercept of the required line is 3, the point is (3,0).
Hence equation of the required line is
y – 0= -7 (x – 3); y + 7x = 21 or 7x + y – 21 = 0

Answer 22.
a. (x+1, y-2) = (3, 1) x+l=3; x=2 y-2 = i; y=3
b. AxB = { (1,4),( 1,6),( 1,9), (2,4), (2,6), (2,9),(3,4),
(3,6), (3,9), (4,4), (4,6) ,(4,9), (5,4), (5,6), (5,9)}
R = {(5,4)}
c. A real function R is to be a modulus function, if f (x) = | x |, x ∈ R, is known as modulus function.

Answer 23.
a. ii (-2, 3)
b. 2x + y = 4

Solution region:
2x + y ≥ 4
⇒ 0 ≥ 4, which is false. || by putting x = 0, y = 0
Hence shade the half plane, which does not contain the origin. x + y < 3
⇒ 0 ≥ 3, which is true.
Hence shade the half plane, which contains the origin.
2x – 3y < 6
⇒ 0 ≤ 6, which is true.
Hence shade the half plane, which contains the origin. The common region shown in the figure ’ is the solution region.

Answer 24.
a. i. When word start with P and end with S, then there are 10 letters to be arranged of which T appears two times.

ii. When there are always 4 letters between P & S
P & S can be at
1st and 6^th place
2nd and 7^th place
3rd and 8^th place
4^th and 9^th place
5^th and 10^th place
6^th and 11^th place
7^th and 12^th place
So, P & S will placed in 7 ways & can be arranged in 7 x 2 ! = 14
The remaining 10 letters with 2T’s 10!
can be arranged in\(\frac { 10i }{ 2i } \)=1814400 ways
The required number of arrangements = 14 x 1814400 = 25401600
b. Can be done in 5 ! ways, such that xGxGxGxGxGx
where G represents the seats for girls and cross mark represents the seats for boys = Total number of ways

Plus One Maths Previous Year Question Papers and Answers

Kerala Plus One Maths Model Question Paper 1

Time Allowed: 2 1/2 hours
Cool off time: 15 Minutes
Maximum Marks: 80

General Instructions to Candidates :

• There is a ‘cool off time’ of 15 minutes in addition to the writing time .
• Use the ‘cool off time’ to get familiar with the questions and to plan your answers.
• Read instructions carefully .
• Read questions carefully before you answering.
• Calculations, figures and graphs should be shown in the answer sheet itself.
• Malayalam version of the questions is also provided.
• .Give equations wherever necessary.
• Electronic devices except non programmable calculators are not allowed in the Examination Hall.

Questions 1 to 7 carry 3 score each. Answer any 6.

Question 1.
Write the set \(\left\{ \frac { 1 }{ 2 } ,\frac { 2 }{ 3 } ,\frac { 3 }{ 4 } ,\frac { 4 }{ 5 } ,\frac { 5 }{ 6 } ,\frac { 6 }{ 7 } \right\} \) r in the set- builder form.
a. If A and B are two sets such that A ⊂ B , then what is A ∪ B
b. There are 200 individuals with a skin disorder, 120 had been exposed to the chemical C₁ 50 to the chemical C₂, and 30 to both the chemicals C₁ and C₂. Find the number of individuals exposed to Chemical C₁ but not chemical C₂.

Question 2.
A lamp post is situated at the middle point M of the side AC of a triangular plot ABC with BC=7m CA = 8m, AB = 9m. Lamp post subtends an angle 15° at the poiny B. Determine the height of the lamp post.

Question 3.
Find square root of the complex number 8- i6.

Question 4.
Arathi took 3 examinations in an year. The marks obtained by her in the second and third examinations are more than 5 and 10 respectively than in the first examination. If her average mark is at least 80 find the minimum mark that she should get in the first examination?

Question 5.
a. A die is thrown until a six comes up. Write down the sample space for this experiment.
b. What is the probability of getting a doublet in throws of a pair of dice.

Question 6.
(a) A hyperbola with a = b is known as…………..

A. rectangular hyperbola
B. isosceles hyperbola
C. equilateral hyperbola
D. None of these

(b) Find the equation of an ellipse whose length of major axis is 26 and foci (± 5, 6)

Question 7.

Questions from 8 to 17 carry 4 score each. Answer any 8.

Question 8.

Question 9.
Let P(n) be the statement : 1³ + 2³ + 3³ +………+n³
 \(={ \left[ \frac { n(n+1) }{ 2 } \right] }^{ 2 }\)
a.Verify whether the statement is true for n = 1
b. Prove the result by using mathematical induction

Question 10.
a. Express (5 – 3i)³ in the form a + ib
b. Solve the equation -x² + x – 2 = 0

Question 11.
Solve the folowing linear inequalities graphically:

Question 12.
a. How many 3 digit even number can be formed form the digits 1,2,3,4,5 and 6, if the digits can be repeated?
b. In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?

Question 13.
a. The base of an equilateral triangle with side 2 a lies along they-axis such that the mid-point of the base is at the origin. Find vertices of the triangle….
b. Find the equation of the line passing through (-3, 5) and perpendicular to the line through the points (2, 5) and (-3, 6)

Question 14.
a. find the centere and radius of the circle x²+ y² – 8x + 10y – 12 = 0
b. Find the equation of the circle passing through (0,0) and making intercepts a and b on the coordinate axes.

Question 15.
a. If p is the length of perpendicular from the origin to the line whose intercepts on the exes are a and b, then show that

b. If the lines 2x + y-3=0, 5x + ky -3=0 and 3x – y-2=0 are concurrent, find the value of k.

Question 16.
a. Find the octant in which the points (-3,1,2) and (-3,1,-2) lie.
b. Find the coordinates of a point on y-axis which are a distance of 5√2 from the point P (3,-2,5)

Question 17.
a. Write the negation of the following statement: If you do all the exercises in this book, you get an A grade in the class,
b. Verify by the method of contradiction, p: √2 is irrational.

Questions from 18 to 24 carry 6 score each. Answer any 5.

Question 18.
a. Draw the graph of the function f: R→ R defined by f(x) = x³ x ∈ R
b. If set A has 2 elements and set B has 3 elements, then the number of function from A to B is
(i) 64
(ii) 6
(iii) 9
(iv) 8

Question 19.
a. If sec x = 13/5, x lies in fourth quadrant, find other t-functions.
b. Prove that show that tan 3x tan 2x tan x = tan 3x – tan 2x – tan x
c. Find the value of tan π/8

Question 20.
a. Find the sum of the sequence 7, 77, 777,  7777, ………….. to n terms.
b. Find the sum of first n terms of the series: 3 x 1² + 5 x 2² + 7 x 3²+…….

Question 21.
a. Find the middle term in the expansion of

b. Find the term independent in the expansion of

Question 22.
a. Find the derivative of x sin x form first principles.

Question 23.
a. Find mean deviation about median for the following data.

b. Calculate mean, variance and standard deviation of the following distribution:

Question 24.
Four cards are drawn from a well shuffled pack of 52 cards. Find the probability that it contains
a. all aces
b. atmost 2 aces
c. atleast two aces

Answers

Answer 1.

Answer 2.

Answer 3.
– 15 – 8i
Let \(\sqrt { 8-6i } \) = x + iy……….. (1)
Squaring we have,
8 – i6=(x + iy)² = x² + i²xy + i²y² = (x² – y²)  +i2xy
Equating the real and imaginary parts, we have
x² – y²= 8 ………….. (2)
2xy = – 6 ……………….. (3)
We know that (x² + y²)²
= (x² – y²)² + 4x² y²
= (8)²+(-6)²= 64+36 = 100
∴ x² + y² = 4m = √100 = 10 ………….. (4)
(2) + (4) we have,
x² -y²  = 8 x² + y² = 10 2x² = 18
x² = 9 ⇒ x = ± 3
In (4), we have, 3²+y²=10 ⇒ y²
=10 – 9 = 1 ⇒ y = ± 1
Since 2xy = -6,
When x = 3, y = -1 and when x = -3, y = 1
3-i and -3 + i are the square roots.

Answer 4.
Let the mark in the first exam = x
Mark in the second exam = x+5
Mark in the third exam = x + 10 x + x + 5 + x + 10.

x >75
Minimum mark Arathi should get in the first exam = 75.

Answer 5.
a. s = {6,(1,6),(1, 1, 6),….,(2, 6),(2, 1, 6),…. }
b. n (s) = 36
doublets are (1,1), (2,2), (3,3),
(4,4),(5,5) and (6,6)
∴ P (getting a doublet) =  \(\frac { 6 }{ 36 } \) = \(\frac { 1 }{ 6 } \)

Answer 6.
a. C.
b. 2a = 26 => a = 13
foci = (±5,0) => c = 5
But c² = a²– b² ⇒ b² =a² – c² = 13²-5² = 144

Answer 7.

Answer 8.

Answer 9.

Answer 10.
a. (5 – 3i)³ = 5³ – 3 x 5²(3i)+3 x 5(3i)²– (3i)³
= 125 – 225i+ 135i² – 21 i³
= 125 – 225i+ 135(-1)-27(-i)
= 125 – 225i – 135 + 27i
= -10 – 198i
b. -x² + x + 2 = 0
a = 1 ; b = 1 ; c = 2
D = b² – 4ac = (1)² – 4 (-1) (2)
= 1 – 8 = -7 < 0

Answer 11.

The shaded region is the solution region.

Answer 12.
a. Here unit place can filled in three ways (i.e. by 2, 4, 6), whereas tens and hundred place can be filled in 6 ways.
b. Out of available nine courses, two are compulsory, Hence the student is free select 3 courses out of 7 remaining courses. Then the number if ways of selecting courses out of 7 courses

Answer 13.
(a) Let ABC be the given equilateral triangle with side 2a. Assume that base BC lies along the y-axis such that the mid-point of BC is at the origin. i.e., BO = OC = a, where O is the origin Now, it is clear that the coordinates of point B are (-a, 0) and C are (a,0), while the coordinates of point. Using Pythagoras theorem to ΔAOC, we obtain
AC² = OA² + OC² (2a)²
= OA²+ a² 4a²– a² = OA²
⇒ OA² =3a² ⇒ OA = √3a

∴ co-ordinates of A are (±√3a ,0). Thus, the vertices of the given equilat­eral triangle are (0, a),(0,-a), and (√3a,0) or (0, a), (0, -a), and (-√3a ,0)
(b) Any line through (-3,5) is y-5 = m(x-(-3)) = m(x + 3) Slope of line joining (2, 5) and (-3, 6) =

∴  slope of a line⊥ to it = 5
∴reqd. line is y-5 = 5(x+3)
⇒ 5x – y + 20=0

Answer 14.
a. centre = (-g, -f) = (4, -5)

b. Equation is
(x₁ – x) (x – x₂)+(y₁ – y) (y – y₁)
(x – a)(x – 0)+(y – 0)(y – b) = 0
x²-ax + y² – by = 0
x² + y² – ax -by = 0

Answer 15.
a. The equaton of line making intercepts a and b on the axes is

(intercept from) ….(i)
Given p = perpendicular distance from

b. Three lines are said to be concurrent, if they pass through a common point, i.e., point of intersection of any two lines lies on the third line. Here given lines are
2x + y – 3 = 0 ……….. (1)
5x + ky – 3 = 0……….. (2)
3x – y – 2 = 0 …………. (3)
Solving (1) and (3) by cross – multipli­cation method, we get,

Therefore, the point of intersection of two lines is (1, 1). Since above three lines are concurrent, the point (1, 1) will satisfy equation (2) so that
5.1+k.1- 3 = 0 ⇒ k = -2.

Answer 16.
a. (-3,1,2) – 2^nd octant
(-3,1,-2) – 6^th octant
b. Let A (0,y,0) be a point on y-axis having distance 5 √2 from (3,-2,5)

⇒ y² + 4y – 12 = 0
⇒ (y + 6) (y-  2) =0
⇒ y = -6,2
∴ A(0,-6,0) and ,4(0,2,0) are the required points

Answer 17.
a. If you do not do all the exercises in this book, you will not get an a grade in the class.
b. Let us assume that be rational.
∴ √2 = a/b_, where a and b are co-prime,
i.e., a an b have no other common factors except 1.
Then 2b² = a² ⇒ 2 divides a.
∴ there exists an integer ^tk^> such that a – 2k
∴ 2b² = 4k² ⇒ 4k² = 2b² = 2k² = ⇒ b²=⇒ 2 divides b.
i.e., 2 devides both a and b, which is contradiction to our assumption that a and b have no common factor.
∴ our supposition is wrong.
∴  √2 is an irrational number.

Answer 18.
a.

b. (iii) n(b)^n(A) =3² = 9

Answer 19.



Answer 20.
a. This is not a G.P., however, we can relate it to a G.P by writing the terms as S_n =7 + 77 + 777 + 7777 + …….. to n terms

b. Let T_n denote the n^th term of the given series

Answer 21.
a. Here n = 10 is even
Middle term \(\frac { 10 }{ 2 }\) +1 = 6^th term

Since we have to find a term indepen­dent of x, i.e., term not having x, so

Answer 22.



Answer 23.
a. We have

b. We first make the data continuous by making classes as below :

Answer 24.

Plus One Maths Previous Year Question Papers and Answers

Kerala Plus One Maths Previous Year Question Paper 2017

Time Allowed: 2 hours
Cool off time: 15 Minutes
Maximum Marks: 60

General Instructions to Candidates

• There is a ‘cool off time’ of 15 minutes in addition to the writing time of 2 hrs.
• Your are not allowed to write your answers nor to discuss anything with others during the ‘cool off time’.
• Use the ‘cool off time’ to get familiar with the questions and to plan your answers.
• Read questions carefully before you answering.
• All questions are compulsory and only internal choice is allowed.
• When you select a question, all the sub-questions must be answered from the same question itself.
• Calculations, figures and graphs should be shown in the answer sheet itself.
• Malayalam version of the questions is also provided.
• Give equations wherever necessary.
• Electronic devices except non programmable calculators are not allowed in the Examination Hall.

Question 1.
Worker population ratio is……………
a. Population / Worker
b. Worker / Population
c. Population / Worker X 100
d. Worker/Population X 100

Question 2.
List any four effects which ‘the miracle seeds’ created in Indian agriculture.

Question 3.
For a classroom discussion, Ashna collected the following information about present In­dia.
a. Infant, mortality rate – 45
b. Life expectancy-66.4
c. Overall literacy level 74.04
d. Compare them with the British period and comments.

Question 4.
Demographic data on birth and death rates in India, a collected and published by………………
a. RG
b. NSSO
c. CSO
d. Labour Bureau

Question 5.
Distinguish between bar diagram and histo­gram. (Hint: Not to draw diagrams)

Question 6.
The various ranks secured by Merin and Kanchana in four medical entrance examinations are

Calculate the rank correlation and interpret the result.

Question 7.
Find the one which is NOT measured for im­proving agricultural market system.
a. Adoption of green revolution
b. Assurance of minimum support price
c. Maintenance of buffer stock
d. Public distribution system

Question 8.
a. Name the system of farming that restores, maintain and enhance Ecological balance,
b. Point out any three merits of it.

Question 9.
Prepare an essay on various policies and pro­grams towards poverty alleviation in India. Do you find any faults in the implementation of these programs? Substantiate.

Question 10.
A value of correlation coefficient (r) =+1.2 in­dicates
a. Perfect+ve correlation
b. High degree of +ve correlation
c. Low degree of +ve correlation
d. Error in calculation

Question 11.
Identify the names of the steps in a project to which you can include the following statisti­cal tools you have studied.


Question 12.
State the two senses in which the word ‘sta­tistics’ is used. Elucidate.

Question 13.
An import substitution policy.
a. Increase in the tax on imported goods
b. Fixing of quotas
c. Enlarge domestic production
d. All of these

Question 14.
a. Name the outcome of the two policy strat­egies of liberalization and privatization,
b. Do you think that Indian agriculture sec­tor was adversely affected by the reform process? Justify.

Question 15.
State to which country the following demo­graphic features belongs to.
(Hint: India, China or Pakistan)
a. Highest annual growth of population
b. Lowest population density.
c. Less urbanization
d. High fertility rate

Question 16.
Observe the graph. It is……..
a. Uni-modal data
b. Bi-model data
c. Multi-modal data
d. None of these

Question 17.
Calculate the Consumer Price Index (CPI)

Question 18.
“Most of the surveys conducted in India are sample surveys”.
Prepare any three reasons to support the above statement.”

Question 19.
Which is NOT a pair?
a. Tapas Majumdar Committee’ – Education
b. Brundtland Commission – Sustainable de­velopment
c. Karve Committee-Agriculture
d. VKRVRao-National income estimation

Question 20.
a. Name the relative measure of standard de­viation.
b. Define SD.
c. Calculate the standard deviation from the following data:

Question 21.
Do India faces challenges in the power sec­tor? Elucidate.

Question 22.
For conducting a survey among 200 house­holds, Anumitha has written the names of all 200 households on pieces of paper, mixed well and 20 names are selected one by one. It is
a. Census method
b. Random sampling
c. Nonrandom sampling
d. None of these

Question 23.
While preparing a frequency distribution from the raw data, name the questions we have to address. Briefly, explain in 1 % pages. (Hint: Four steps in the construction of a frequency distribution)

Question 24.
The heights (in cm) of 11 plants in a garden are

a. Choose the mode.
b.Calculate the mean and median height of the plants, by using the equations.

Question 25.
Which one of the following statements is NOT TRUE about the employment sector in India?
a. 93% workers are in the informal sector.
b. 50% of the workers are self- employed.
c. Disguised and seasonal unemployment exist in the Indian farm sector.
d. During 1972-2010 there was a movement of workers from casual wage to self-empl­oyment.

Question 26.
Define the term, ‘Sustainable development’. Suggest various strategies for attaining it in two pages.

Question 27.
Express your view in the following aspects with reference to the present human capital formation in India.
a. Education for all
b. Gender equity
c. Higher education

Question 28.
The current and base year prices of a group of commodities are Rs. 180 and Rs. 135 re­spectively. It shows
a. price is said to have risen by 38.33%
b. price is decreased by 33.33%
c. price is increased by 133.33%
d. none of these

Answers

Answer 1.
Worker /population X 100

Answer 2.

• Enable India to attain sufficiency in food grains.
• Increased market surplus
• Large-scale increase in production
• Price of food grains declined.
• Government procured surplus products for future use.

Answer 3.
a. 218/1000
b. 32 years
c. Less than 16 %

Answer 4.
RGI (also give merits for NSSO)

Answer 5.

Bar diagram	Histogram
Bar diagram comprised agro up of equispaced	A histogram is a two dimen­sional diagram
Equal width rectangular bars	The width may be different
Space is left between adjent bar	No space is left
Draw for discrete and con­tinues variables.	Drawn for continuous vari­able only
Not help to determine any average	Help to determine made

Answer 6.

R1 Exams	R2 Rank of Merin	Rank of Kanchana	(D = R1 R2)	d2
KEAM	1	2	-1	1
AIPMT	3	4	-1	1
JIPMER	2	4	-1	1
ALLMS	4	1	3	9
			12

Answer 7.
a. Adoption of green revolution

Answer 8.
a. Organic farming
b. Substitute with locally produced and or­ganic inputs

• More nutritional value
• Pesticide-free
• Highly international demand
• Environment-friendly

Answer 9.
1. Rural Employment Generation Programme.
It is implemented through the Khadi and vil­lage Industries Commission (KVIC), To help eligible enterpreneurs to set up village indus­try units. Under this programme, enterpre­neurs can establish village industries by avail­ing of margin money assistance from KVIC and loans from public sector scheduled com­mercial banks, selected regional rural banks. Under REGP, bank appraises the projects as per the scheme and take credit decision.

2. Prime Minister’s Rozgar Yojana (PMRY): In this programme help to set up any kind of enterprise that generates employment to the educated unemployed from low income fami­lies in rural and urban areas.

3. Swarna Jayanthi Shahari Rozgar Yojana (SJSRY)
The urban self-employment Programme and the urban Wage Employment Programme are two special scheme of the SJSRY, initiated in December 1997.

4. National Food for Work Programme (NFWP)
This Programme was introduced February 2001 for five months and was further extend­ed. This programe aims at augmenting food security through wage employment in droug­ht affected rural areas.

5. Swarna Jay at hi Gram Swarozgar Yojana (SJGSY)

It was launched with effect from 1999. As a result of amalgamating certain erstwhile prog­rammes into a single self-employment pro­gramme. This programme aims at promoting micro-enterprises and helping the rural poor into Self Help Groups(SHG). This scheme cov­ers all aspect of self-employment.

6. Mid Day Meals Scheme: In this programme involves provision for free lunch on working days for children in primary and upper primary classes in government education centers. The primary objective of the scheme is to provide hot cooked meal to children of primary and upper primary.

7. National Social Assistance Programme (NSAP): It was introduced on 15 August 1995 as a 100% centrally sponsored scheme for social assistance to poor household affected by old age, death of primary bread earner and mater­nity.

8. Pradhan Mantri Gramodya Yojana (PMGY): It was started in 2001. It aims at improving the standard of living of the rural people by de­veloping five important area health primary education, drinking water, housing and roads.

9. Pradhan Mantri Gram Sadak Yojana (PMGSY): It was nationwide plan in india to provide good all-weather road connectivity to unconnected villages. The scheme has started to change the lifestyle of many villagers.

10.Sampoorna Gramin Rozgar Yojana (SGRY): It was introduced in 2001. Jawahar Gram Samridhi yojana and Employment Assurance Scheme were intergrated into a single yojana. The objective of this yojana is to provide em­ployment opportunity to the surplus Workers. Through the policy towards poverty alleviati­on has evolved in a progressive manner but over the last five and a half decades it has not undergone any radical transformation.

The three major area of concern which preve­nt the successful implementation of the progra­ms, they are:

• These program depend mainly on govern­ment and bank officials for their implementa­tion since such officials are ill motivated, the resources are inefficiently used and wasted.
• Unequal distribution of land and other as­sets due to the benefits have been availed by the non-poor.
• In comparison to the magnitude of poverty, the amount of resource allocated for these programmes is not sufficient.

Answer 10.
Error in calculation

Answer 11.
b. Analysis on interpretation
c. organisation or presentation of data

Answer 12.
In the plural sense:- statitics refers to the sys­tematic collection of numerical facts. It indic­ated information in terms of numbers or nume­rical data such as employment statistics and population statistics.
In the singular sense:- statistics refers to the science of studying statistical methods. It indic­ates the techniques or methods of collecting organising, presenting analysing and inter­preting data.

Answer 13.
d. All of these

Answer 14.
a. Globalisation
b. Yes, Reduction of public investment. There has been a drastic decrease in the volume of public investment. In the agricultural sector. There has been an acute outback from the Indian government to provide. Sufficient irri­gation facilities, electricity information sys­tem, market linkages and roads.

Removal at subsidies removal subsidies on fertilisers pushed up the cost of production of agriculture. This made forming more expen­sive, thereby, adversely affecting the poor and marginal farmers. Shift towards cash crops and lack of food grai­ns. The export-oriented production strategies led to the shift of agricultural production from food grains to the production of cash crops like cotton jute etc.

Liberalisation and reduction in impart duties on agricultural products. Due to adherence to the to commitment, Indian government re­duced impart duties on agricultural products that forced the poor and marginal farmers to complete with their foreign countries part in international markets.

Answer 15.
a. Pakistan
b. China
c. India
d. Pakistan

Answer 16.
b. Bi-modaldata

Answer 17.

Item	Weight(4%)	Base year price	Current year price
food	50	2000	3000
cloth	15	1000	1200
fuel	25	400	700
Rent	10	500	600

Item	Weight W	Base year Price	Current year Price	R p1/p0l00	WR
food	50	2000	3000	150	7500
cloth	15	1000	1200	120	1800
fuel	25	400	700	175	4375
Rent	10	500	600	120	1200
Total	100				14875

Consumer price index = \(\cfrac { \Sigma WR }{ \Sigma W } =\cfrac { 14875 }{ 100 } =148.75\)

Answer 18.

• A sample can give recomable, reliable and accurate informations.
• Lower cost
• Shorter time
• More detailed information can be collected as sample is less than population.
• Need smaller loan of enumerators
• Easier to trains and supervise the enum­erators

Answer 19.
c. Karve Committee – Agriculture

Answer 20.
a. Coefficient of variables
b. Standard Deviation
Standard Deviation: is the positive square root of the mean of squared deviations from mean.
So if there are five values X₁, X₂, X_3,X₄and X5, first their mean is calculated. Then devia­tions of the values from mean are calculated. These deviation are then squared. The mean of these squared deviations is the variance. Positive square root of the variance is the standard deviation.
c.

Marks	No. of students	X	d(x-5)	fd	fd2 (Fd x d)
0-10	3	5	-30	-90	2700
10-20	5	15	-20	-250	2000
20-30	6	25	-10	100	600
3040	8	35	0	0	0
40-50	10	45	10	100	1000
50-60	1	55	20	20	400
60-70	5	65	30	360	10800
70-80	5	75	40	200	8000
	50			430	25,500

Answer 21.
Yes.

1. Installed capacity to generate electricity is not sufficient to feed the annuval demand of7%
2. State electricity board are running is losses of Rs,’ 500 billion transmission and distri­bution loss, wrong price, inefficiency etc.
3. Challenge from the part of the private sector and foreign power generates.
4. General public interest due to high tariff and long power

Answer 22.
b. Random sampling

Answer 23.

• Find the range of data
• Decide the approximate number of classes
• Determine the approximate class interval size
• Decide the starting point
• Determine the remaining class limits
• Distribute the data into respective classes.

Answer 24.

Answer 25.
During 1972 -2010 there was a movement of workless from casual wage to self-empl­oyment.

Answer 26.
It refers to the development strategy to inte­rruption till the resource extraction was not above the rate of regeneration of the resource and the wastes generated were within the assimilating capacity of the environment But today, environment fails to perform its third and vital function of the substance resulting in an environmental crisis. The rising popula­tion of the developing countries and the af­fluent consumption and production stand­ards of the developed world have placed huge stress on the environment in terms of its first two functions.

Strategies for sustainable Development.

1. Use of a non-conventional source of energy: – India heavily, depends on the hydropower plants to meet its power needs. Both of the­se have adverse environmental impacts. Thermal power plants emit large quantities of carbon dioxide, which is a greenhouse gas. It is not used properly.

2. Bio-Composting:-Inorder to increase pro­duction, we have started using chemical fertilisers which are adversely affecting the waterbodies, groundwater system, etc. But again farmers in large numbers have started using organic fertilisers for production.

3. Mini-Hydel Plants:- Mountainous region have streams everywhere, Most of such streams are perennial. Mini-hydel plants use the energy of such streams to move small turbines which generates electrici­ty. Such power plants are more or less envi­ronment friendly.

4. Traditional Knowledge and Practices:- Traditionally, Indian people have close to their environment. If we look back at our agriculture system, healthcare system, ho­using, transport, etc we find that all prac­tices have been environment-friendly.

5. Biopest Control:-With the advent of Gre­en Revolution, the country entered into the use of chemical pesticides to produce more which laid the adverse impacts on soil, wa­ter bodies, milk, meat, and fishes. To meet this challenge, better methods of pest control should be brought. One step is pesti­cides based on plants like neem. Even many animals also help in controlling pests like snakes, peacocks, etc.

6. CNG in Urban Areas:- In Delhi, the use of Compressed Natural Gas as fuel in the public transport system has significantly low­ered air pollution and the air has become cleaner in the last few years.

Answer 27.
a. It is still a dream
b. Better than before
c. A few takes

Answer 28.
d.None of these

Plus One Maths Previous Year Question Papers and Answers

Students can Download Chapter 3 Principles of Programming and Problem Solving Questions and Answers, Plus One Computer Application Chapter Wise Questions and Answers helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus One Computer Application Chapter Wise Questions Chapter 3 Principles of Programming and Problem Solving

Plus One Computer Application Principles of Programming and Problem Solving 1 Mark Questions and Answers

R Programming MCQ PDF arranged chapterwise! Start practicing now for exams, online tests.

Question 1.
The process of writing program is called _______.
Answer:
programming or coding.

Question 2.
One who writes program is called ______.
Answer:
Programmer.

Question 3.
The step by step procedure to solve a problem is known as ______.
Answer:
Algorithm.

Question 4.
Diagrammatic representation of an algorithm is known as ______.
Answer:
Flow .

Question 5.
Program errors are known as ______.
Answer:
bugs.

Question 6.
Process of detecting and correcting errors is called ________.
Answer:
debugging .

Question 7.
Mr. Ramu represents an algorithm by using some symbols. This representation is called ______.
Answer:
Flow Chart.

Question 8.
Your computer teacher asked you that which symbol is used to indicate beginning or ending flow chart? What is your answer?
a) Parallelogram
b) Rectangle
c) Oval
d) Rhombus
Answer:
c) Oval.

Question 9.
You are suffering from stomach ache. The doctor prescribes you for a scanning. This process is related in a phase in programming. Which phase is this ?
Answer:
Problem identification.

Question 10.
Your friend asked you a doubt that to draw a flow chart parallelogram is used for what purpose?
Answer:
input /output.

Question 11.
Mr. Anil wants to perform a multiplication which symbol is used to represent in a flow chart.
Answer:
It is a processing so rectangle is used.

Question 12.
Mr. George wants to check a number is greater than zero and to perform an operation while drawing a flow chart which symbol is used for this?
Answer:
Rhombus

Question 13.
ANSI means ______.
Answer:
American National Standards Institute.

Question 14.
To indicate the flow of an operation which symbol is used to draw a flow chart.
Answer:
Flow lines with arrow heads .

Question 15.
Mr. Johnson is drawing a flow chart but it is not fit in a single page. Which symbol will help him to complete the flow chart?
Answer:
Connectors.

Question 16.
Mr. Ravi developed a S/W student information system, He wants to protect the s/w from unauthorized copying. There is an act what is it?
Answer:
Copy right act.

Question 17.
Odd man out.
a) Parallelogram
b) Oval
c) Rectangle
d) Star
Answer:
d) Star, others are flowchart symbols.

Question 18.
Odd man out.
(a) Oval
(b) Rhombus
(c) Connector
(d) Triangle
Answer:
Triangle, Others are flowchart symbols.

Question 19.
Raju wrote a program and he wants to check the errors and correct if any? What process he has to do for this?
Answer:
process, debugging.

Question 20.
Odd one out.
a) Problem identification
b) Translation
c) debugging
d) copy right
Answer:
d) Copy right, others are phases in programming.

Question 21.
Odd man out.
a) syntax error
b) logical error
c) Runtime error
d) printer error
Answer:
d) Printer error, Others are different types of errors.

Question 22.
A computerized system is not complete after the execution and testing phase? What is the next phase to complete the system?
Answer:
Documentation.

Question 23.
Mr. Sathian takes a movie DVD from a CD library and he copies this into another DVD without per-mission. This process is called ______.
Answer:
Piracy.

Question 24.
Mr. Santhosh purchased a movie DVD and he takes several copies without permission. He is a _______.
a) Programmer
(b) Administrator
c) Pirate
(d) Organizer
Answer:
c) Pirate.

Question 25.
The symbol used for copy right is a _____.
a) &
(b) Copy
(c) #
(d) ©
Answer:
d)©

Question 26.
Following are the advantages of flowcharts one among them is wrong. Find it.
a) Better communication
b) Effective analysis
c) proper program documentation
d) Modification easy
Answer:
d) Modification easy, It is a disadvantage.

Question 27.
Which flow chart symbol has one entry flow and two exit flows?
Answer:
Diamond.

Question 28.
Which flow chart.symbol is always used in pair?
Answer:
connector.

Question 29.
Program written in HLL is called ______.
Answer:
Source code.

Question 30.
Some of the components in the phases of programming are given below. Write them in order of their occurrence.
a) Translation
b) Documentation
c) Problem identification
d)Coding of a program
Answer:
The chronological order is as follows
1) c) Problem Identification
2) d) Coding of a program
3) a) Translation
4) b) Documentation

Question 31.
a) ________ is the stage where programming errors are discovered and corrected.
Answer:
Debugging or compiling.

Question 32.
compilation and execution there were no errors. But he got a wrong output. Name the type of error he faced.
Answer:
Logical Error.

Question 33.
Pick out the software which rearranges the scattered files in the hard disk and improves the performance of the system.
a) Backup software
b) File compression software
c) Disk defragmenter 1
d) Anti virus software
Answer:
Disk defragmenter.

Question 34.
Some phases in programming are given below.
1) Source coding
2) Execution
3) Translation
4) Problem study
These phases should follow a proper order.
Choose the correct order from the following:
a) 4 —> 2 —> 3 —> 1
b) 1 —> 3 —> 2 —> 4
c) 1 —> 3 —> 4 —> 2
d) 4 —> 1 —> 3 —> 2
Answer:
d)4 —> 1 —> 3 —> 2

Question 35.
Which one of the following errors is identified at the time of compilation?
a) Syntax error
b) Logical error
c) Run-time error
d) All of these
Answer:
a) Syntax error.

Question 36.
Pick the odd one out and give a reason for your finding:

Answer:
c) This has one entry flow and more than one exit flow
OR
b) Used for both input and output..

Plus One Computer Application Principles of Programming and Problem Solving 2 Marks Questions and Answers

Question 1.
A debate on ‘Whether Free Software is to be promoted’ is planned in your class. You are asked to present points in support of Free Software. What would be your arguments, (at least three)?
Answer:
Freedom to use Comparatively cheap Freedom to modify and redistribute.

Question 2.
Mr. Roy purchased a DVD of a movie and he found that on the cover there is a sentence copy right reserved and a mark ©. What is it? Briefly explain?
Answer:
It is under the act of copy right and the trade mark is © copy right 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.

Question 3.
Can a person who knows only Malayalam talk to a person who knows only Sanskrit normally consider the corresponding situation in a computer program and justify your answer?
Answer:
Normally it is very difficult to communicate. But it is possible with the help of a translator. Translation is the process of converting programs written in High Level Language into Low Level Language (machine Language). The compiler or interpreter is used for this purpose. It is a program.

Question 4.
Define the term, debugging. Write the names of two phases that are included in debugging.
OR
Define the different types of errors that are encountered during the compilation and running of a program
Answer:
Debugging :- The program errors are called ‘bugs’ and the process of detecting and correcting errors is called debugging.
Compilation and running are the two phases.
OR
In general there are two types of errors syntax errors and logical errors. When the rules or syntax of the language are not followed then- syntax errors occurred and it is displayed after compilation. When the logic of a program is wrong then logical errors occurred and it is not displayed after compilation but it is displayed in the execution and testing phase.

Question 5.
Write an algorithm to input the scores obtained in three unit tests and find the average score.
OR

Explain the flow chart and predict the output.
Answer:
Step 1 : Start
Step 2 : Read S1, S2, S3
Step 3 : avg = S1 + S2 + S3/3
Step 4 : Print avg
Step 5 : Stop.
OR
This flowchart is used to print the numbers as 1,2,3, ……… 30

Question 6.
Differentiate between top down design and bottom up design in problem solving
Answer:
Bottom up design : Here also larger programs are divided into smaller ones and the smaller ones are again subdivided until the lowest level of detail has been reached. We start solving from the lowest module onwards. This approach is called Bottom up design.

Question 7.
Answer any one question from 5 (a) and 5 (b).
Draw a flowchart for the following algorithm.
Step 1 : Start
Step 2 : Input N
Step 3 : S=0, K=1
Step 4 : S = S +K
Step 5 : K = K +1
Step 6 : If K < = N Then Go to Step 4
Step 7 : Print s
Step 8 : Stop
OR
Name the two stages in programming where debugging process is involved. What kinds of errors are removed in each of these stages?
Answer:
a)

b) The two stages are compile time and run time. In the debugging process can remove syntax . error, logical error and runtime error.

Question 8.
Answer any one question from 7(a) and 7(b) .
a) Observe the following portion of a flowchart. Fill in the blank symbols with proper instructions to get 321 as the output.

b) The following flowchart can be used to print the numbers from 1 to 100. Identify another problem that can be solved using this flowchart and write the required instructions in the symbols.

Answer:
The following flowchart can be used to store another problem such as used to print odd numbers less than 200.
a)

b) The following flowchart can be used to store another problem such as used to print odd numbers less than 200.

Question 9.
Write an alogorithm to print the numbers upto 100 in reverse order, That is the output should be as 100, 99, 98, 97,… .1
OR
Draw a flow chart to check whether the given number is positive, negative or zero.
Answer:
Step 1 : Start
Step 2 : Set i < — 100
Step 3 : if i<=0 then go to step 6
Step 4 : Print i.
Step 5 : Set i < — i – 1 go to step 3
Step 6 : Stop

Plus One Computer Application Principles of Programming and Problem Solving 3 Marks Questions and Answers

Question 1.
When you try to execute a program, there are chances of errors at various stages, Mention the types of errors and explain.
Answer:
1) syntax error :
eg : 5=x
2) Logic error. If the programmer makes any logical mistakes, it is known as logical error.
Eg: To find the sum of values A and B and store it in a variable C you have to write C=A+B. Instead of this if you write C=A*B, it is called logic error.
3) Runtime error : An error occured at run time due to inappropriate data.
Eg: To calculate A/B a person gives zero to B. There is an error called division by zero error during run time.

Question 2.
Following is a flow chart to find and display the largest among three numbers. Some steps are missing in the flowchart. Redraw the flow chart by adding necessary.steps and specify its purpose. How can this flow chart be modified without using a fourth variable?
Answer:

Question 3.
A flow chart is given below.

a) What will be the output of the above flow chart ?
b) How can you modify the above flow chart to display the even numbers upto 20, starting from 2.
Answer:
a) 1,2,3,4,5.

Question 4.
Write an algorithm to check whether the given number is even or odd.
Answer:
step 1 : Start
Step 2 : Read a number to N
Step 3 : Divide the number by 2 and store the remainder in R.
Step 4 : If R = O Then go to Step 6
Step 5 : Print “N is odd” go to step 7
Step 6 : Print “N is even”
Step 7 : Stop

Question 5.
Write an algorithm to find the largest of 2 numbers?
Answer:
Step 1 : Start
Step 2 : Input the values of A, B
Step 3 : Compare A and B. If A> B then go to step 5
Step 4 : Print” B is largest” go to Step 6.
Step 5 : Print “A is largest”
Step 6 : Stop

Question 6.
Write an algorithm to find the sum of n natural numbers and average?
Answer:
Step 1 : Start
Step 2 : Set i 1, S 0
Step 3 : Read a number and set to n
Step 4 : Computer i and n if i>n then go to step 7.
Step 5 : Set S <— S+ i
Step 6 : i <— i+1 go to step 4
Step 7 : avg 4<— S/n Step 8 : Print “Sum = S and average = avg” Step 9 : Stop Question 7. Write an algorithm to find the largest of 3 numbers.
Answer:
step 1 : Start
Step 2 : Read 3 numbers and store in A,B,C
Step 3 : Compare A and B. lfA>B then go to Step 6
Step 4 : Compare B and C if C>B then go to Step 8
Step 5 : print “B is largest” go to Step 9
Step 6 : Compare A and C if Q>A then go to Step 8
Step 7 : Print” A is largest” go to Step 9
Step 8 : Print “C is largest”
Step 9 : Stop

Question 8.
Write an algorithm to calculate the simple interest (I =P*N*R/100)
Answer:
Step 1 : Start
Step 2 : Read 3 values for P,N,R
Step 3 : Calculate I <— P*N*R/100
Step 4 : Print “The simple interest = I
Step 5  : Stop

Question 9.
Write an algorithm to calculate the compound interest (C. I = Px(1 +r/100)n – P)
Answer:
Step 1 : Start
Step 2 : Read 3 number for p,n,r
Step 3 : Calculate Cl = p x(1+r/100)n – p
Step 4 : Print “The compound Interest = C.I”
Step 5 : Stop

Question 10.
Write an algorithm to find the cube of first n natural numbers .(eg:1,8,27 …….. n³)
Answer:
Step 1 : Start
Step 2 : Set i <— 1
Step 3 : Read a number and store in n
Step 4 : Compare rand n if i>n then go to step 7
Step 5 : Print i*i*i
Step 6 : i <— i+1 go to step 4
Step 7 : Stop

Question 11.
Write an algorithm to read a number and find its factorial (n!=n*(n-1)*(n-2) * …..3*2*1)
Answer:
Step 1 : Start
Step 2 : Fact <—1
Step 3 : Read a number and store in n
Step 4 : If n=0 then go to step 7
Step 5 : Fact <— Fact *n
Step 6 : n <— n-1 go to step 4
Step 7 : Print “Factorial is fact”
Step 8 : Stop.

Question 12.
Draw a flow chart to find the sum of n natural numbers and average.
Answer:

Question 13.
Draw a flow chart to find the largest of three numbers.
Answer:

Question 14.
Draw a flow chart to find the largest of two numbers.
Answer:

Question 15.
Draw a flow chart to check whether the given number is even or odd.
Answer:

Question 16.
Draw a flow chart to calculate the simple interest.
Answer:

Question 17.
Draw a flow chart to calculate compound interest.
Answer:

Question 18.
Draw a flow chart to find the cube of n natural numbers (1,8,27 …….n³)
Answer:

Question 19.
Draw a flow chart to read a number and find its factorial.
Answer:

Question 20.
Mr. Vimal wants to represent a problem by using a flowchart, which symbols are used for this. Explain.
Answer:



These symbols will help us to complete the flow chart, which is not fit in a single page. A connector symbol is represented by a circle and a letter or digit is placed within the circle to indicate the link.

Question 21.
Jeena uses algorithm to represent a problem while Neena uses flowchart which is better? Justify your answer?
Answer:
Flow chart is better. The advantages of flow chart is given below.
1. Better communication:- A flow chart is a pictorial representation while an algorithm is a step By step procedure to solve a program. A programmer can easily explain the program logic using a flow chart.
2. Effective analysis :- The program can be analyzed effectively through the flow chart.
3. Effective synthesis :- If a problem is big it can be divided into small modules and the solution for each module is represented in flow chart separately and can be joined together to get the final system design.
4. Proper program documentation :- A flow chart will help to create a document that will help the company in the absence of a programmer.
5. Efficient coding :- With the help of a flow chart it is easy to write program by using a computer language.

Question 22.
A flow chart is a better method to represent a program. But it has some limitation what are they?
Answer:
The limitations are given below
1) To draw a flowchart, it is time consuming and laborious work.
2) If any change or modification in the logic we . may have to redraw a new flow chart.
3) No standards to determine how much detail can include in a flow chart.

Question 23.
Match the following,

Answer:
1 – e
2 – a
3 – d
4 – f
5 – b
6 – c

Question 24.
Alvis executes an error – free program but he got an error. Explain different types of error in detail.
Answer:
There are two types of errors in a program before execution and testing phase.They are syntax error and logical error. When the programmer violates the rules or syntax of the programming language then the syntax error occurred.
Eg: It involves incorrect punctuation. Key words are used for other purposes, violates the structure etc. It detects the compiler and displays an error message that include the line number and give a clue of the nature of the error. When the programmer makes any mistakes in the logic, that types of errors are called logical error. It does not detect by the compiler but we will get a wrong output.
The program must be tested to check whether it is error free or not. The program must be tested by giving input test data and check whether it is right or wring with the known results. The third type of errors are Runtime errors, this may be due to the in appropriate data while execution. For example consider B/C. If the end user gives a value zero for c, the execution will be interrupted because division by zero is not possible. These situation must be anticipated and must be handled.

Question 25.
The following are the phases in programming. The order is wrong rearrange them in correct order.
1. Debugging
2. Coding
3. Derive the steps to obtain the solution
4. Documentation
5. Translation
6. Problem identification
7. Execution and testing
Answer:
The correct order is given below.
1. Problem identification
2. Derive the steps to obtain the solution
3. Coding
4. Translation
5. Debugging
6. Execution and testing
7. Documentation

Question 26.
Draw a flow chart to input ten different numbers and find their average. ‘
Answer:

Question 27.
Draw the flow chart to find the sum of first N natural numbers.
Answer:

Question 28.
Make a flow chart using the given labelled symbols, for finding the sum of all even numbers upto ‘N’

Answer:
Draw flowchart in any of the following order
e, c, d, f, i, h, a, b, g
e, d,c, f, i, h, a, b, g
e, c, d, a, f, i, h, b, g
e, d, c, a, f, i, h, b, g
Step 1 : Start
Step 2 : Input n
Step 3 : i = I
Step 4 : if i<=n/2 then repeat step 5 & 6
Step 5 : if n%i = = 0 print i
Step 6 : i = i + I
Step 7 : Stop

Question 29.
List the two approaches followed in problem solving or programming. How do they differ?
Answer:
Approaches in problem solving Top down design : Larger programs are divided into smaller ones and solve each tasks by performing simpler activities. This concept is known as top down design in problem solving Bottom up design : Here also larger programs are divided into smaller ones and the smaller ones are again subdivided until the lowest level of detail has been reached: We start solving from the lowest module onwards. This approach is called Bottom up design. Phases in Programming

1) Problem identification : This is the first phase in programming. The problem must be identified then only it- can be solved, for this we may have to answer some questions. During this phase we have to identify the data, its type, quantity and formula to be used as well as what activities are involved to get the desired out put is also identified for example if you are suffering from stomach ache and consult a Doctor. To diagnose the disease the Doctor may ask you some question regarding the diet, duration of pain, previous occurrences etc, and examine some parts of your body by using stethoscope X-ray, scanning etc.

2) Deriving the steps to obtain the solution: There are two methods, Algorithm and flowchart, are used for this.
a) Algorithm :- The step-by-step procedure to solve a problem is known as algorithm. It comes from the name of a famous Arab mathematician Abu Jafer Mohammed Ibn Musaa Ai-Khowarizmi, The last part of his name Al-Khowarizmi was corrected to algorithm.
b) Flowchart :- The pictorial or graphical representation of an algorithm is called flowchart.

Question 30.
Write an algorithm to find the sum of the squares of the digits of a number. (For example, if 235 is the input, the output should be 22+32+52=38)
Answer:
Step 1 : Start
Step 2 : Set S = O
Step 3 : Read N
Step 4 : if N > O repeat step 5, 6 and 7
Step 5 : Find the remainder. That is rem =N%10
Step 6 : S = S + rem * rem
Step 7 : N = N/10
Step 8 : Print S
Step 9 : Stop

Question 31.
Consider the following algorithm and answer the following questions:
Step 1 : Start
Step 2 : N=2, S=0
Step 3 : Repeat Step 4, Step 5 while N<=10
Step 4 : S=S+N
Step 5 : N=N+2
Step 6 : Print S
Step 7 : Stop
a) Predict the output of the above algorithm.
b) Draw a flowchart for the above algorithm
Answer:
a) The output is 30

Question 32.
“It is better to give proper documentation within the program”. Give a reason.
Answer:
It is the last phase in programming. A computerized system must be documented properly and it is an ongoing process that starts, in the first phase and continues till its implementation. It is helpful for the modification of the program later.

Plus One Computer Application Principles of Programming and Problem Solving 5 Marks Questions and Answers

Question 1.
Mr. Arun wants to develop a program to computerize the functions of super market. Explain different phases he has to under go is detail.
OR
Briefly explain different phases in programming.
Answer:
The different phases in programming is given below:
1) Problem identification : This is the first phase in programming. The problem must be identified then only it can be solved, for this we may have to answer some questions.
During this phase we have to identify the data, its type, quantity and formula to be used as well as what activities are involved to get the desired out put is also identified for example if you are suffering from stomach ache and consult a Doctor. To diagnose the disease the Doctor may ask you some question regarding the diet, duration of pain, previous occurrences etc, and examine some parts of your body by using stethoscope X-ray, scanning etc.

2) Deriving the steps to obtain the solution. There are two methods, Algorithm and flowchart, are used for this.
a) Algorithm :- The step-by-step procedure to solve a problem is known as algorithm. It comes from the name of a famous Arab mathematician Abu Jafer Mohammed Ibu Musaa Al-Khowarizmi, The last part of his name Al-Khowarizmi was corrected to algorithm.
b) Flowchart:- The pictorial or graphical representation of an algorithm is called flow-chart.

3) Coding The dummy codes (algorithm)or flow-chart is converted into program by using a computer language such s Cobol, Pascal, C++, VB, Java etc.

4) Translation The computer only knows ma-chine language. It does not know HLL, but the human beings HLL is very easy to write pro. grams. Therefore a translation is needed to convert a program written in HLL into machine code. (object code). During this step, the syntax errors of the program will be displayed. These errors are to be corrected and this process will be continued till we get “No errors” message. Then
it is ready for execution.

5) Debugging The program errors are called ‘bugs’ and the process of detecting and correcting errors is called debugging. In general there are two types of errors syntax errors and logical errors. When the Riles or syntax of the language are not followed then syntax errors occurred and it is displayed after compilation. When the logic of a program is wrong then logical errors occurred and it is not displayed after compilation but it is displayed in the execution and testing phase.

6) Execution and Testing In this phase the program will be executed and give test data for testing the purpose of this is to determine whether the result produced by the program is correct or not. There is a chance of another type of error, Run time error, this may be due to in-appropriate data.

7) Documentation It is the last phase in programming. A computerized system must be documented properly and it is an ongoing process that starts in the first phase and continues till its implementation. It is helpful for the modification of the program later.

Question 2.
Briefly explain the characteristic of an algorithm.
Answer:
The following are the characteristics of an algorithm
1) It must starts with ‘start’ statement and ends with ‘stop’ statement.
2) it should contains instructions to accept input and these are processed by the subsequent instructions.
3) Each and every instruction should be precise and must be clear. The instructions must be possible to carry out, for example consider the examples the instruction “Go to market” is precise and possible to carried out but the instruction “Go to hell” is also precise and can not be carried out.
4) Each instruction must be carried out in finite time by a person with paper and pencil.
5) The number of repetition of instructions must be finite.
6) The desired results must be obtained after the algorithm ends.

Kerala State Board New Syllabus Plus One Malayalam Textbook Answers Unit 1 Chapter 4 Matsyam Text Book Questions and Answers, Summary, Notes.

Kerala Plus One Malayalam Textbook Answers Unit 1 Chapter 4 Matsyam

Matsyam Questions and Answers

Matsyam Summary

Kerala State Board New Syllabus Plus One Malayalam Textbook Answers Unit 3 Chapter 1 Kavyakalaye Kurichu Chila Nireekshanangal Text Book Questions and Answers, Summary, Notes.

Kerala Plus One Malayalam Textbook Answers Unit 3 Chapter 1 Kavyakalaye Kurichu Chila Nireekshanangal

Kavyakalaye Kurichu Chila Nireekshanangal Questions and Answers

Kavyakalaye Kurichu Chila Nireekshanangal Summary

Kerala State Board New Syllabus Plus One Malayalam Textbook Answers Unit 2 Chapter 4 Kaippad Kelkkunnundo? Text Book Questions and Answers, Summary, Notes.

Kerala Plus One Malayalam Textbook Answers Unit 2 Chapter 4 Kaippad Kelkkunnundo?

Kaippad Kelkkunnundo? Questions and Answers

Kaippad Kelkkunnundo? Summary

Kerala State Board New Syllabus Plus One Malayalam Textbook Answers Unit 4 Uravu Text Book Questions and Answers, Summary, Notes.

Kerala Plus One Malayalam Textbook Answers Unit 4 Uravu

Uravu Questions and Answers

Uravu Summary

Kerala State Board New Syllabus Plus One Malayalam Textbook Answers Unit 3 Chapter 4 Lathiyum Vediyundayum Text Book Questions and Answers, Summary, Notes.

Kerala Plus One Malayalam Textbook Answers Unit 3 Chapter 4 Lathiyum Vediyundayum

Lathiyum Vediyundayum Questions and Answers

Lathiyum Vediyundayum Summary

Kerala State Board New Syllabus Plus One Maths Chapter Wise Previous Questions and Answers Chapter 8 Binomial Theorem.

Kerala Plus One Maths Chapter Wise Previous Questions Chapter 8 Binomial Theorem

Plus One Maths Binomial Theorem 3 Marks Important Questions

Question 1.
i) The number of terms in the expansion of \(\left(\frac{x}{3}+9 y\right)^{10}\) is _____.(IMP-2013)
ii) Find the middle term in the above expansion.
Answer:
i) 11

Question 2.
i) Find the general term in the expansion of (x + y)ⁿ
ii) Find the middle term in the expansion of \(\left(2 x+\frac{1}{3 y}\right)^{18}\) (MARCH-2014)
Answer:

Question 3.
i) Write the general term in the expansion of (a + b)ⁿ 
ii) Find the 9th term in the expansion of \(\left(\frac{x}{2}+\frac{6}{x^{2}}\right)^{12}\) (IMP-2014)
Answer:

Plus One Maths Binomial Theorem 4 Marks Important Questions

Question 1.
i) Find the general term in the expansion of \(\left(3 x^{2}-\frac{1}{3 x}\right)^{9}\) (MARCH-2010)
ii) Find the term independent of x in the above expansion.
Answer:

Get the free “Expanding Binomial Calculator” widget for your website.

Question 2.
Consider the expansion of \(\left(x^{2}-\frac{1}{3 x}\right)^{9}\) (IMP-2010)
i) Find the coefficient of x⁹
ii) Find the term which is independent of x.
Answer:

Question 3.
Consider the expansion of \(\left(\frac{x}{9}+9 y\right)^{2 n}\) (MARCH-2011)
i) The number of terms in the expansion is _____
(a) 2n
(b) n+1
(c) 2n+1
(d) 2/7-1
ii) What is its (n+1)^th term?
iii) If n = 5, find its middle term.
Answer:

Question 4.
i) Write the general term in the expansion (1 + x)⁴⁴   
Write 21st and ,22nd terms in the expansion of (1 + x)⁴⁴
iii) If 21^st and 22^nd terms in the expansion of (1 + x)⁴⁴ are equal then find the value of x. (IMP-2011)
Answer:

Question 5.
8. Find(x + y)⁴ – (x – y)⁴. (IMP-2012)
Hence evaluate: (√5 + √6)⁴ – (√5 – √6)⁴
Answer:

Question 6.
i) How many terms are there in the expansion of (1 + x)²ⁿ (n is a positive integer)? (IMP-2012)
ii) Show that the middle term in the (1 + x)²ⁿ
expansion of is \(\frac{1.3 .5 \ldots(2 n-1)}{n !} 2^{n} x^{n}\)
Answer:

Question 7.
i) Find the general term in the expansion of \(\left(\frac{x}{2}-\frac{2}{x}\right)^{10}\) (MARCH-2012)
ii) Find the terms independent of x in the above expansion.
Answer:

Question 8.
i) Find the number of terms in the expansion of \(\left(x-\frac{1}{x}\right)^{14}\) (MARCH-2013)
ii) Find the general term in the expansion of \(\left(x-\frac{1}{x}\right)^{14}\)
iii) Find the term independent of x in the above expansion.
Answer:
i) 15

Question 9.
i)Write the number of terms in the expansion of (a -b)²ⁿ
ii) Find the general term in the expansion of \(\left(x^{2}-y x\right)^{12}, x \neq 0\) (MARCH-2014)
iii) Find the coefficient of x⁶y³ in the expansion of (x + 2y)⁹
Answer:

Question 10.
i) Write the expansion of (a + n)ⁿ, where n is any positive integer. (IMP-2014)
ii) Find the value of ‘a’ if the 17^th term and 18^th term in the expansion of (2 +a)⁵⁰ are equal.
Answer:

Question 11.
i) The number of term in the expansion of \(\left(x-\frac{1}{x}\right)^{2 n}\) is ______. (MARCH-2015)
(a) n+1
(b) n
(c) 2n+1
(d) 2n+2
ii) Find a, if the 17^th term and 18^th term of the expansion of (2 +a)⁵⁰ are equal.
Answer:

Question 12.
i) Number of terms in the expansion of \(\left(x+\frac{1}{x}\right)^{20}\) (IMP-2016)
(a) 19
(b) 20
(c) 21
(d) 22
Consider the expansion of \(\left(3 x^{2}-\frac{1}{3 x}\right)^{9}\)
find the coefficient of x⁶ and the term independent of x.
Answer:

Question 13.
The 8th term in the expression (MARCH-2016)
of(√2 + √3)⁷ is
a) 27√2
b) 27√3
c) 72√2
d) 72√3
ii) Find the term independent of x in the expansion of \(\left(x+\frac{1}{2 x}\right)^{18} ; x>0\)
Answer:

Question 14.
Write the expansion of (a + b)^{4  (MAY-2017)}
Evaluate: (√5 + √6)4+ (√5 – √6)⁴
Answer:

Question 15.
Consider the expansion of \(\left(x+\frac{1}{x}\right)^{10}\) (MARCH-2017)
i) The number of terms in the expansion is _____.
(a) 10
(b) 9
(c)11
(d) 12
ii) Find the term which is independent of x in the above expansion.
Answer:

Plus One Maths Binomial Theorem 6 Marks Important Questions

Question 1.
i) Write the number of terms in the expansion of (a + b)ⁿ
ii) Expand \(\left(\frac{x}{3}+\frac{1}{x}\right)^{5}\) (MARCH-2013)
iii) Find the general term in the expansion of \(\left(x^{2}-y\right)^{6}\)
Answer: