Plus Two

Kerala State Board New Syllabus Plus Two Economics Chapter Wise Previous Questions and Answers Part I Chapter 5 Market Equilibrium.

Kerala Plus Two Microeconomics Chapter Wise previous Questions Chapter 5 Market Equilibrium

Question 1.
Compared to rural areas, the wage rate is higher in urban areas. Discuss the reasons for this. (MARCH-2008)
Answer:
Wages are higher in urban areas compared to rural areas due to the following reasons.

• Availability of skilled workers in urban areas.
• Professionals in urban areas.
• Occupational and geographical mobility.
• Differences in risks in certain urban jobs.

Question 2.
When you conducted a survey among teachers working in parallel colleges in Trichur district it is found that there exists a difference in earnings among teachers teaching different subjects. Find the reason for the same with suitable examples. (MAY-2009)
Answer:
Wage differences are due to the following reasons.

• Difference in skill and productivity
• People are not the same in matter of tastes, talents and efficiency.
• Occupational and geographical mobility.
• Some professions require high cost and long period of training.
• Difference in risks involved in certain jobs.
• Due to these reasons, some are paid more and others are paid less.

Question 3.
Suppose the demand and supply curve of good x shift simultaneously. The simultaneous shift can happen in four possible cases. The impact on equilibrium price and quantity in all four cases is different. On the basis of this, complete the following table : (MARCH-2010)

Answer:
a) Leftward
b) Rightward
c) Decrease
d) Increase

Question 4.
Under fixed price analysis of a product market, if quantity supplied is either in excess or falls short of quantity demanded price will change because of excess supply or demand. In this occasion (MARCH-2010)
a) How the equilibrium is determined?
b) Name the principle.
Answer:
a) Assume that the elasticity of supply is infinite that is the supply schedule is horizontal. In this situation the equilibrium output will be solemnly determined by aggregate amount of demand at this price in the economy.
b) Keynesian analysis or effective demand Principle.

Question 5.
The demand function of a monopoly firm is given as q = 20 – 2P, substitute the values of P from 10 to 1. (MAY-2010)
a) Calculate the demand schedule of the commodity.
b) From the table calculate the TR, AR and MR values in a tabular form.
c) Draw the AR and MR curve in same set of axis.
d) When the price elasticity is more than one?
Answer:
a)

b)

c)

d) Price elasticity is more than one when MR is positive.

Question 6.
Find the correct term for the following : (MAY-2010)

Answer:
a) Equilibrium price
b) Price ceiling

Question 7.
The Government imposed lower limit on the price that may charged for a particular good is called price floor. Give two examples for imposition of price floor. The Government imposed lower limit on the price that may charged for a particular good is called price floor. Give two examples for imposition of price floor (MAY-2010)
Answer:
i) Price floor fixed for paddy
ii) Price floor fixed for food grains

Question 8.
This is a demand curve for a branded umbrella. (MARCH-2011)
a) If the demand for umbrella increases during rainy season, what term we use in economics to denote this change? Draw the curve.
b) What you call this change when the price of umbrella increased, the demand decreased.

Answer:
a) Rightward shift or increase in demand

b) Upward movement along the same demand curve or there is contraction of demand.

Question 9.
The demand and supply equations of a commodity in a perfectly competitive market are given as qd = 700 – P qs = 500 + 3P (MARCH-2011)
Calculate:
a) Equilibrium price
b) Equilibrium quantity
c) Based on the given supply and demand equations draw equilibrium situation on a diagram.
Answer:
a) Equilibrium price

b) Equilibrium quantity
qd = 700 – P
= 700 – 50
= 650
c)

Question 10.
Imposition of the price ceiling below the equilibrium price leads to (MARCH-2012)
a) Excess demand
b) Excess supply
c) Deficit demand
d) Deficit supply
Answer:
a) Excess demand

Question 11.
Match the following: (MARCH-2012)

Answer:

Question 12.
Welfare considerations enable the govt, to impose price floor for some goods and services. Mention any one example of imposition of price floor. (MARCH-2013)
Answer:
In India, floor prices are fixed for a variety of commodities like paddy, rubber, wheat, coconut etc.

Question 13.
The following diagram shows equilibrium market price determined by the equality between demand and supply. (MARCH-2013)
Show the effect of change in demand and supply on equilibrium price and output under the following situations (use diagrams)
i) Increase in demand or when the demand curve shift rightwards.
ii) Increase in supply or when supply curve shift rightwards.

Answer:
i) When demand curve shifts to right (increase in demand), there will be increase in equilibrium price and increase in equilibrium quantity. This change is shown in the diagram.

ii) When supply curve shifts to right (increase in supply), the equilibrium price decreases and the equilibrium quantity increases. This is given in the following diagram.

Question 14.
Diagrammatically illustrate the impact of (MAY-2014)
a) Price ceiling and
b) Price floor on market equilibrium
Answer:
a) Price Ceilings
A price ceiling occurs when the government puts a legal limit on how high the price of a product can be. In order for a price ceiling to be effective, it must be set below the natural market equilibrium.
When a price ceiling is set, a shortage occurs. For the price that the ceiling is set at, there is more demand than there is at the equilibrium price. There is also less supply than there is at the equilibrium price, thus there is more quantity demanded than quantity supplied. An inefficiency occurs since at the price ceiling quantity supplied the marginal benefit exceeds the marginal cost. This inefficiency is equal to the dead weight welfare loss.

This graph shows a price ceiling. P* shows the legal price the government has set, but MB shows the price the marginal consumer is willing to pay at Q*, which is the quantity that the industry is willing to supply. Since MB > P* (MC), a dead weight welfare loss results. P’ and Q’ show the equilibrium price. At P* the quantity demanded is greater than the quantity supplied. This is what causes the shortage,
b) Price Floors
A price floor is the lowest legal price a commodity can be sold at. Price floors are used by the government to prevent prices from being too low. The most common price floor is the minimum wage the minimum price that can be payed for labor. Price floors are also used often in agriculture to try to protect farmers.

Question 15.
From the list of goods given below, find out the one which cannot be provided through market mechanism? (MARCH-2015)
a) Private goods
b) Public goods
c) Merit goods
d) Club goods
Answer:
b) Public goods

Question 16.
The following diagram shows the equilibrium price of wheat determined by the supply curve ‘SS’ and market demand curve ‘DD’. With the help of the diagram answer the questions given below. (MARCH-2015)
a) If the Government imposes price ceiling on wheat, what happens to the demand for wheat?
b) Define price ceiling.
c) Write down two adverse impacts of price ceiling on the consumers.

Answer:

Question 17.
Explain through a diagram the effect of a rightward shift (increase) of both the demand and supply curves on the equilibrium price and quantity? (MAY-2015)
Answer:
When demand curve shifts to right (increase in demand), there will be increase in equilibrium price and increase in equilibrium quantity. This change is shown in the diagram.

When supply curve shifts to right (increase in supply), the equilibrium price decreases and the equilibrium quantity increases. This is given in the following diagram.

Question 18.
List the 3 different ways in which an oligopoly firm may behave. (MARCH-2016)
Answer:
If the market of a particular commodity consists of more than one seller but the number of sellers is few, the market structure is termed oligopoly. The special case of oligopoly where there are exactly two sellers is termed duopoly. We shall explain the different ways in which the oligopoly firms may behave.
Firstly duopoly firms may collude together and decide not to compete with each other and maximize total profits of the two firms together. In such a case the two firms would behave like a single monopoly firm that has two different factories producing the commodity.
Secondly, take the case of a duopoly where each of the two firms decide how much quantity to produce by maximizing its own profit assuming that the other firm would not change the quantity that it is supplying. We can examine the impact using a simple example where both the firms have zero cost.
Thirdly, some economists argue that oligopoly market structure makes the market price of the commodity rigid, i.e., the market price does not move freely in response to changes in demand.

Question 19.
Explain the consequence if price prevailing in the market is fixed: (MARCH-2016)
i) Above the equilibrium price (Price floor)
ii) Below the equilibrium price (Price ceiling)
Answer:
i) Excess supply
ii) Excess demand

Question 20.
Demand and supply equations of commodity X is given by (MARCH-2016)
qd = 100- P
qs = 70 + 2P
find the equilibrium price and quantity.
Answer:

Question 21.
Imposition of price floor leads to (MAY-2016)
a) an excess demand
b) an excess supply
c) normal demand
d) any of the above
Answer:
b) an excess supply

Question 22.
State whether the following statements are true or false: (MAY-2016)
a) With supply curve remaining unchanged, when demand curve shifts rightward, the equilibrium quantity decreases and equilibrium price decreases.
b) In a perfectly competitive market, equilibrium occurs where market demand equals market supply.
Answer:
a) False
b) True

Question 23.
Suppose onion price increases above ₹100 per kg and the government imposes price ceiling. (MAY-2016)
a) What is price ceiling?
b) What are the consequence of imposing price ceiling?
Answer:
a) Price ceiling mean maximum price. It is the maximum price fixed by the government. The aim of price ceiling is to protect consumers. Government fixes price ceiling for essential products and medicines to protect the interests of the consumers.
Consequence of imposing price ceiling:
1. Black marketing
2. Malpractices by fair price shops
3. Sale of inferior quality goods.

Question 24.
Suppose the demand and supply functions of wheat are given by Q_D = 800 – 4P and Q_S= 600 + 4P respectively.
i) Find the equilibrium price and quantity demanded. (MARCH-2017)
ii) Due to a shortage of fertilizers, the cost of production of wheat is increased. So that the new supply function is
Q_S = 400 + 4P. What will happen to the equilibrium price and quantity demanded?
Answer:


The equilibrium price will increase and equilibrium quantity will fall.

Question 25.
How does equilibrium price and quantity demand affect when (MARCH-2017)
i) Both demand and supply curves shift in the same direction.
ii) Demand and supply curves shift in the opposite directions.
Answer:
i) Both demand and supply curve shift in the same direction.
When the demand curve and supply curve shift to right: For a given price, more quantity is demanded as well as more quantity is supplied. The demand curve and supply curve shifted to right to show a greater quantity for a given price. If supply increases relatively greater than the equilibrium price is smaller, but if demand increases relatively greater than the intersection is higher and the price obtained will be higher. Only than it is certain that there will be more quantity at new equilibrium price.

When the demand curve and supply curve shifts to left: The price may increase or decrease depending whether supply decreases relatively more or demand decrease relatively more, respectively, and the only certainty is that there is less quantity at new equilibrium point

ii) Demand curve shifts left and supply curve shifts right: Demand decreases and supply increases. The price was fallen, but if supply curve shifts a lot more right than the demand curve shifts left, then the new equilibrium point will mean more quantity is supplied at a much lower price.

Demand curve shifts right and supply curve shift left: Demand increases and supply decreases. The price will increase but depending on how far the supply curve shifts left, the equilibrium quantity would be more or less or same. This shift will see a higher equilibrium point with less quantity demand.

Kerala State Board New Syllabus Plus Two Economics Chapter Wise Previous Questions and Answers Part I Chapter 4 The Theory of The Firm Under Perfect Competition.

Kerala Plus Two Microeconomics Chapter Wise previous Questions Chapter 4 The Theory of The Firm Under Perfect Competition

Question 1.
Correct the following statements, if necessary: (MARCH-2010)
Statement I : Liquidity trap is the situation in which speculative demand for money is infinitely elastic.
Statement II : The imposition of a unit tax shift the supply curve of a firm to the left.
Statement III : The profit level that is just cover the explicit cost and opportunity cost is supernormal profit.
Answer:
Statement I : No correction
Statement II : No correction
Statement III : The profit level that is just cover
the explicit cost and opportunity cost is normal profit

Question 2.
There are three identical firms in the market. The following table shows the supply schedule of a firm : (MARCH-2010)

1) Define market supply
2) Compute market supply schedule
3) Draw market supply curve
Answer:
1) The output level that firms in the market produce in aggregate, corresponding to different values of market prices.
2)

3) Draw a market supply curve that slopes upwards corresponding to the above values.

Question 3.
Any factor that affects a firm’s marginal cost curve is of course a determinant of its supply curve”, there are three factors – determining the supply curve of a firm. Identify them. (MAY-2010)
Answer:
Factors determining the supply curve of a firm are :
Technical progress
Input prices
Unit tax

Question 4.
Mr. Kameth is a textile mill owner. He is facing challenges in production and marketing screnario. The situations he faced are given in column A and corresponding outcomes in marginal cost and supply of output are given in column B and C. Match A with B and C. (MARCH-2011)

Answer:

Question 5.
Under perfect competition a firm’s profit in the short run is maximized when 3 conditions are satisfied. (MARCH-2011)
a) Discuss the 3 conditions.
b) From the following schedule, suggest profit
maximizing level of output in the short run if price is ₹10.

Answer:
a 1) MC must be equal to MR
2. MC must cut MR from below
3. Slope of MC must be greater than slope of MR.
b)

c) Since MC = MR = 10 at 6th unit of output, the profit maximising level of output is 6 units.

Question 6.
In the following diagram, at points E and E₁ MC and MR are equal. Among these, which point do you consider as producer’s equilibrium? Justify your answer. (MARCH-2012)

Answer:
In this diagram, producer’s equilibrium is at point E_r This is because this point satisfies all the conditions of equilibrium. The conditions for attaining equilibrium are,
i) MC = MR
ii) MC must cut MR from below
These two conditions are satisfied at point E₂.

Question 7.
Firm ‘A’ is operating under the condition of perfectly competitive market. Whether firm ‘A’ is capable of maintaining abnormal profit in the long run? Why? Hint: Long run equilibrium of a firm under perfect competition. (MARCH-2012)
Answer:
Yes, I do agree to the statement that a firm cannot make supernormal profit in the long run under perfect competition. This is because; freedom of entry will prevent super normal profit in the long run.
We first determine the firm’s profit-maximizing out-put level when the market price is greater than or equal to the minimum (long run) AC. This done, we determine the firm’s profit-maximizing output level when the market price is less than the minimum (long run) AC.
Case 1: Price greater than or equal to the minimum LRAC
Case 2: Price less than the minimum LRAC Combining cases 1 and 2, we reach an important conclusion. A firm’s long run supply curve is the rising part of the LRMC curve from and above the minimum LRAC together with zero output for all prices less than the minimum LRAC.

Question 8.
State whether the statements are true or false. (MARCH-2013)
i) In a perfect competitive market structure, firms are price takers.
ii) All firms in the market produce homogeneous product.
Answer:
i) True
ii) True

Question 9.
In an economy, the level of income is Rs. 1,000 crores and the MPC is 0.8. If the investment increases by 200 crores. Calculate the total increase in income. (MARCH-2013)
Answer:

Total increase in income is K x 200 Crores
That is 5 x 200 Crores = 1,000 Crores
Total increase in income = 1,000 Crores

Question 10.
Under perfect competition, a firm will not produce output level in cases under (MARCH-2013)
a) P > MC and
(b) P< MC. If so, what is the condition of profit maximising output in the short run. Give diagramatic illustration. (Hint: Short run equilibrium of a firm under perfect competition).
Answer:
Perfect Competition – Short Run Equilibrium In the model of price and output determination under perfectly competitive market conditions, price is determined by the impersonal market forces of supply and demand, and not by individual actions of buyers and sellers. The individual firm in such a market may be said to be a price-taker. Perfect competition is used by economists not so much as an attainable goal, but as a pure state against which all other markets can be measured.
For a market to be perfectly competitive, the following necessary conditions must, in general, prevail.
1) There must be many firms acting independently. Each firm is small enough relative to the size of the market, so that a single firm’s decision to either stop production entirely or to produce to full capacity will not have any perceptible effect on market supply to cause a change in market price.
2) Entry and exit from the market are free and frictionless for both the firms and consumers.
3) The products offered for sale are homogeneous and divisible into small units.
5) Buyers and sellers have perfect knowledge about the market conditions.
6) Price is determined by the impersonal market forces of supply and demand, and not by individual actions of buyers and sellers. The individual firm in such a market may be said to be a price-taker.
7) There is perfect knowledge among consumers about the price at which goods are being sold in the market. Sellers thus cannot manipulate the commodity price and thereby exploit the consumer.
8) There is perfect mobility of goods and factors of production among firms. Uniformity in factor prices is prevalent in the market.
If these necessary conditions prevail, the firm can lose its entire market if it sets its price above the market price. It can also expect no gain by lowering price, since it can sell all it wishes to produce at the market price. The competitive firm has no price discretion. Market price will not be affected by the independent action of a single firm. No firm is able to influence market price.
The objective of each firm is to maximize profit. Profit is the difference between revenue and cost of production. Marginal cost (MC) is the cost incurred to produce an additional unit of the product. If the per unit price of a commodity is greater than the marginal cost, the firm will be interested in producing more of the commodity. On the other hand if price falls below marginal cost, the firm will curtail its production. Equilibrium condition will prevail at a point where profit is maximized. This happens where price is equal to marginal cost (P = MC). Also at the point of equilibrium, the marginal cost curve must be upward sloping.

In the diagram the given price is P. Again the firm will produce the level of output for which MC = MR. This occurs at point E, giving a level of output of Q. Notice that at this point, AR = AC, so the firm is making normal profit.
So, in the short run, a perfectly competitive firm could be making super normal profit, or a loss, or just normal profit, depending on the given market price. Note that if the firm’s losses get too big in the short run (i.e. AR < AVC) then it will have to shut down.

Question 11. What are the conditions that are to be fulfilled for a firm to be in short run equillibrium under perfectly competitive market conditions? (MAY-2014)
Answer:
A firm is in equilibrium when it has no tendency to change its level of output. It needs neither expansion nor contraction. It wants to earn maximum profits. In the words of A. W. Stonier and D.C. Hague, “A firm will be in equilibrium when it is earning maximum money profits.” ’ Equilibrium of the firm can be analysed in both short- run and long-run periods. A firm can earn the maximum profits in the short run or may incur the minimum loss. But in the long run, it can earn only normal profit. Short-run Equilibrium of the Firm : The short run is a period of time in which the firm can vary its output by changing the variable factors of production in order to earn maximum profits or to incur minimum losses. The number of firms in the industry is fixed because neither the existing firms can leave nor new firms can enter it. It’s Conditions: The firm is in equilibrium when it is earning maximum profits as the difference between its total revenue and total cost. For this, it essential that it must satisfy two conditions:
(1) MC = MR, and
(2) the MC curve must cut the MR curve from below at the point of equality and then rise upwards. The price at which each firm sells its output is set by the market forces of demand and supply. Each firm will be able to sell as much as it chooses at that price. But due to competition, it will not be able to sell at all at a higher price than the market price. Thus the firm’s demand curve will be horizontal at that price so that P = AR = MR for the firm.

Marginal Revenue and Marginal Cost Approach : The short-run equilibrium of the firm can be explained with the help of the marginal analysis as well as with total cost-total revenue analysis. We first take the marginal analysis under identical cost conditions. This analysis is based on the following assumptions:
1) All firms in an industry use homogeneous factors of production.
2) Their costs are equal. Therefore, all cost curves are uniform.
3) They use homogeneous plants so that their SAC curves are equal.
4) All firms are of equal efficiency.
5) All firms sell their products at the same price determined by demand and supply of the industry so that the price of each firm is equal to AR = MR.
Determination of Equilibrium: Given these assumptions, suppose that price OP in the competitive market for the product of all the firms in the industry is determined by the equality of demand curve D and the supply curve S at point E in Figure 1 (A) so that their average revenue curve (AR) coincides with the marginal revenue curve (MR).

Question 12. A fruits seller sells 600 Kg. of grapes at market price of ₹40 per kg. When price increases to ₹50 per kg, he is ready to sell 750kg of grapes. Find out the price elasticity of supply. (MARCH-2015)
Answer:
Elasticity of supply

Question 13.
A firm that maximizes profit under perfect competition will not produce an output where (MARCH-2015)
(a) P > MC and
(b) P<MC.
If so, what is profit maximizing output condition in the short run? Briefly illustrate with diagram.
Answer:
A firm is in equilibrium when it has no tendency to change its level of output. It needs neither expansion nor contraction. It wants to earn maximum profits. In the words of A.W. Stonier and D.C. Hague, “A firm will be in equilibrium when it is earning maximum money profits.”
Equilibrium of the firm can be analysed in both short- run and long-run periods. A firm can earn the maximum profits in the short run or may incur the minimum loss. But in the long run, it can earn only normal profit.
Short-run Equilibrium of the Firm:
The short run is a period of time in which the firm can vary its output by changing the variable factors of production in order to earn maximum profits or to incur minimum losses. The number of firms in the industry is fixed because neither the existing firms can leave nor new firms can enter it.
It’s Conditions:
The firm is in equilibrium when it is earning maximum profits as the difference between its total revenue and total cost.
For this, it essential that it must satisfy two conditions:
(1) MC = MR, and
(2) the MC curve must cut the MR curve from below at the point of equality and then rise upwards.
The price at which each firm sells its output is set by the market forces of demand and supply. Each firm will be able to sell as much as it chooses at that price. But due to competition, it will not be able to sell at all at a higher price than the market price. Thus the firm’s demand curve will be horizontal at that price so that P = AR = MR for the firm.
1. Marginal Revenue and Marginal Cost Approach: The short-run equilibrium of the firm can be explained with the help of the marginal analysis as well as with total cost-total revenue analysis. We first take the marginal analysis under identical cost conditions. This analysis is based on the following assumptions:
1) All firms in an industry use homogeneous factors of production.
2) Their costs are equal. Therefore, all cost curves are uniform.
3) They use homogeneous plants so that their SAC curves are equal.
4) All firms are of equal efficiency.
5) All firms sell their products at the same price determined by demand and supply of the industry so that the price of each firm is equal to AR = MR.
Determination of Equilibrium:
Given these assumptions, suppose that price OP in the competitive market for the product of all the firms in the industry is determined by the equality of demand curve D and the supply curve S at point E in Figure 1(A) so that their average revenue curve (AR) coincides with the marginal revenue curve (MR).

Question 14.
Will a profit-maximizing firm in a competitive market ever produce a positive level of output in the range where the marginal cost is falling? (MAY-2015)
Answer:
No, a profit maximising firm will not produce in the range where the marginal cost is falling. This is because, at this range, his profit is not maximised. So he fixes his level of out output at the point where marginal cost equals marginal revenue.
This can be explained with the help of a diagram.

As per the diagram, if the firm fixes output at the range where MC is falling his profit will not be maximised. Being profit maximising firm, he goes on producing OQ level of output corresponding to the point where MC=MR. This is at the rising part of MC. So his profit is maximised as shown in shaded area.

Question 15.
At the market price of ₹10, a firm supplies 4 units of output. The market price increases to ₹30. The price elasticity of the firm’s supply is 1.25. What quantity will the firm supply at the new price? (MAY-2015)
Answer:

Question 16.
Distinguish: (MARCH-2016)
a) Break even point
b) Shutdown point
Answer:
a) The point on the supply curve at which a firm earns
normal profit is called the break even point. The point of minimum average cost at which the supply curve cuts the LRAC curve is therefore the break even point of a firm.
b) In the short run the firm continues to produce as long as the price remains greater than or equal to the minimum of AVC. Therefore, along the supply curve as we move down, the last price-output combination at which the firm produces positive output is the point of minimum AVC where the SMC curve cuts the AVC curve. Below this, there will be no production. This point is called the short run shutdown point of the firm. In the long run, the shut down point is the minimum of LRAC curve.

Question 17.
Identify the wrong statements and correct the same. (MARCH-2016)
i) A perfectly competitive market deals in heterogeneous product.
ii) Each buyer Under perfect competition is a price taker.
iii) A perfectly competitive market is a market where there is only a single seller.
Answer:
i) Wrong. A perfectly competitive market deals with homogenous products
ii) Wrong. Each seller under perfect competition is a price taker.
iii) Wrong. A monopoly market is the market where there is only a single seller.

Question 18.
A firm under perfect competition wishes to maximize its profit in the short run. State and explain the conditions must hold for profit maximization. (MAY-2016)
Answer:
Perfect competition is a market situation where there are large number of buyers and sellers dealing with homogeneous commodities.
Conditions of equilibrium
i) MC = MR
ii) MC must cut MR from below It can be explained as,

Question 19.
Differentiate between the shut-down point and break even point. (MAY-2016)
Answer:
Shut down point refers to a situation where average revenue is equal to average variable cost. In other words it is the minimum pint of AVC. On the other hand, break even point is the no-profit, no loss point. It is the point where TR = TC or AR = AC.

Question 20.
Which one of the following condition is not satisfied by the long run equilibrium of a firm under perfect condition? (MARCH-2017)
a) P = AR
b) AR = MR
c) MC = MR
d) AFC = AVC
Answer:
AFC = AVC

Question 21.
Graphically explain the short run equilibrium of the firm under Perfect Competition. Draw separate diagram depicting the following conditions: (MARCH-2017)
i) The firm is earning super normal profit.
ii) The firm is earning only normal profit.
iii) The firm is incurring a loss
Answer:
The firm is earning super normal profit
Under perfect competition a firm’s super normal profit in the short run is maximised when 3 conditions are satisfied.
1) Market price P should be equal to marginal cost (MC) at equilibrium output q i.e, MC = MR = P
2) MC should be non-decreasing at Q, i.e. MC should cut MR from below.
3) P ≥ AVC
i) Since at point e AC curve touches AR curve, the firm enjoys normal profit only
ii) The firm is incurring a loss because of the free entry and exit of firms and buyers.
This can be explained with diagram.

Profit maximization under short run graph

Kerala State Board New Syllabus Plus Two Economics Chapter Wise Previous Questions and Answers Part I Chapter 3 Production and Costs.

Kerala Plus Two Microeconomics Chapter Wise Previous Questions Chapter 3 Production and Costs

Question 1.
Classify the following costs into Fixed Costs and Variable costs. (MARCH-2008)
Raw material costs, Daily wages, Interest on capital, Rent, Salary to M.D, Electricity charges, Insurance, Transportation Charges.

Answer:

Question 2.
Following table shows the AC and total quantity of a firm. (MARCH-2008)

a) Complete the table.
b) Plot TFC, TVC and TC on the same set of axis.
c) Write relevant equations to find out AFC, AVC, AC and MC.
Answer:
a)

Question 3.
The cost incurred by a Toys Manufacturing Company is given below. Classify the cost into fixed cost and variable cost. (MARCH-2009)
Rent, Wages, Insurance Premium, Electricity Charges, Cost of raw material, Salary to the Managing Director.

Answer:

Question 4.
The total cost structure of a firm is given in the schedule (MARCH-2009)

a) Fill up the column appropriately from the data given.
b) On the same set of axis plot the AC and MC curves.
Answer:

Question 5.
Total cost of producing 1000 cell phone is ₹10 lakhs if the marginal cost of producing 1001 unit is ₹4,000. What will be the total cost of producing 1001 unit? (JUNE-2009)

Answer:
10,04,000

Question 6.
State whether the following statements are true or false. Rewrite the statement if they are false: (JUNE-2009)
a) TFC is zero at zero level of output.
b) AC is minimum at the point where AC = MC.
c) AVC curve is a rectangular hyperbola.
d) TFC curve is‘U’shaped.
Answer:
a) False. TFC is positive even when the level of output is zero.
b) True
c) False. AVC curve is‘U’ shaped.
d) False. TFC is horizontal straight line.

Question 7.
Reserve Bank of India has increased the bank rate and cash reserve ratio in, June 2008 to control inflationary tendencies in the Indian economy. How ever this effort of RBI became ineffective (JUNE-2009)
Answer:
a) Value of certain products went up and the petroleum prices increased. As a result of it RBI’s efforts to regulate the inflationary pressure failed. Thus monetary policy resulted ineffective.
b) In additional to monetary measures like CRR and bank rate policy, various other measures can be adopted to regulate the economy. Taxation and expenditure policy can be used by the government. Similarly government may provide subsidy or can introduce price ceiling and support prices.

Question 8.
Let the production function of a firm be Q = 3L²K² (MAY-2010)
a) Find out the maximum possible output that the firm can produce with 5 units of L and 3 units of K.
b) What is the maximum possible output that the firm can produce with 10 units of L and zero units of K?
Answer:

Question 9.
“In the long run, the shut down point of the firm is the minimum of LRAC curve.” (MAY-2010)
a) Which is the shut down point of a perfect competitive firm in short run?
b) Draw the diagram to explain the shut down condition of a firm under short run.
Answer:
a) Previously, while deriving the supply curve, we have discussed that in the short run the firm continues to produce as long as the price remains greater than or equal to the minimum of AVC. Therefore, along the down, the last price-output combination at which the firm produces positive output is the point of minimum AVC where the SMC curve cuts the AVC curve. Below this there will be no production. This point is called tiTe short run shutdown point of the firm. In the long run, however, the shut down point is the minimum of LRAC curve.

Question 10.
Correct the figure if there are any mistakes (MARCH-2011)

Answer:

Question 11.
Gireesh cultivates paddy on a piece of land. He employs labourers successively and total product is given here. (MARCH-2011)

a) Complete the given table.
b) Plot TP, APL and MPL on the same set of axis.
c) At what level of total product, the producer stops further employment? (Suggest from schedule)
d) Give reasons.
Answer:


c) 7th labour
d) When 7th labour is employed, TP becomes maximum or MP becomes zero.

Question 12.
The following table shows the TC schedule of a firm. What is the TFC of this firm? Calculate TVC, AFC, AVC, SAC and SMC of the firm. (MARCH-2012)

Answer:

Question 13.
Rajeev is a farmer who produces paddy in his 10 acres of land. He is trying to increase his total output by increasing the quantity of only one of his inputs – say labour. Which law of production explains this situation? What will be the effect on his total output? Give your suggestion to Rajeev with a suitable diagram. (MARCH-2012)
Answer:
Law of Variable Proportions The law of diminishing marginal product says that if we keep increasing the employment of an input, with other inputs fixed, eventually a point will be reached after which the resulting addition to output will start falling. A somewhat related concept with the law of diminishing marginal products is the law of variable proportions. It says that the marginal product of a factor input initially rises with its employment level. But after reaching a certain level of employment, it starts falling.
The reason behind the law of diminishing returns or the law of variable proportion is the following. As we hold one factor input fixed and keep increasing the other, the factor proportions change. Initially, as we increase the amount of the variable input, the factor proportions become more and more suitable for the production and marginal product increases. But after a certain level of employment, the production process becomes too crowded with the variable input and the factor proportions become less and less suitable for the production. It is from this point that the marginal product of the variable input starts falling. Since inputs cannot take negative values, marginal product is undefined at zero level of input employment. Marginal products are additions to total product. For any level of employment of an input, the sum of marginal products of every unit of that input up to that level gives the total product of that input at that employment level. Therefore, total product is the sum of marginal products. Average product of an input at any level of employment is the average of ail marginal products up to that level. Average and marginal products are often referred to as average and marginal returns, respectively, to the variable input.
The marginal product (MP) and total product (TP) of an input are related. The points of relationship are given below.
i) When MP increases, TP also increases
ii) When MP is zero, TP becomes maximum
iii) When MP becomes negative, TP turns negative The relationship between MP and TP are picturised below

Question 14.
The following table shows TFC and TVC of a firm. Find out TC, AFC, AVC, AC and MC of the firm. (MARCH-2013)

Answer:

Question 15.
From the table identify the different levels of TP which makes the different phases of the operation of the law of variable proportions. (MARCH-2013)

Answer:

Question 16.
Short run MC and AC curves are U-shaped. Write down any three relationships between Me and AC. (MAY-2014)
Answer:

marginal cost (MC) is above average cost (AC), the average cost rises, that is, the marginal cost (MC) pulls the average cost (AC) upwards.
ii) When marginal cost (MC) stands equal to the average cost (AC), the average cost remains the same, that is, the marginal cost pulls the average cost horizontally.
iii) if the marginal cost (MC) is below the average cost (AC); average cost falls, that is, the marginal cost pulls the average cost downwards.

Question 17.
‘Short run production functions are fixed proportion production functions’. Do you agree? Substantiate (MAY-2014)
Answer:
Yes, I agree with the statement that Short Run Production Functions are fixed proportion production functions. The short run is a time period where at least one factor of production is in fixed supply. A business has Ghosen it’s scale of production and must stick with this in the short run.
We assume that the quantity of plant and machinery is fixed and that production can be altered by changing variable inputs such as labour, raw materials and energy.
The time periods used differ from one industry to another; for example, the short-run in the electricity generation industry differs from local sandwich bars. If you are starting out in business with a new venture selling sandwiches and coffees to office workers, how long is your long run? It could be as short as a few days – enough time to lease a new van and a sandwich-making machine

Question 18.
Fill in the blanks: (MAY-2014)

Answer:

Question 19.
Which of the following cost will be zero when production is stopped? (MARCH-2015)
a) Average Fixed cost
b) Total Cost
c) Fixed cost
d) Variable cost
Answer:
d) variable cost

Question 20.
The following diagram represents TP, MP and AP curves of a firm. After studying the curves, answer the questions given below. (MARCH-2015)

a) When does ‘TP’ becomes maximum?
b) At what rate (increasing or decreasing) does ‘TP’ increase when ‘MP’ increases?
c) When does ‘MP’ become negative?
Answer:
a) MP becomes zero
b) Increasing rate
c) TP decreases

Question 21.
Following information about a firm is given below: (MARCH-2015)

From the given information estimate,
a) Total Fixed Cost
b) Total Variable Cost
c) Average cost
d) Marginal Cost
Answer:

Question 22.
Consider the following cost schedule of a firm and find AC, AVC and MC. (MAY-2015)

Answer:

Question 23.
“Production is the transformation of inputs into outputs”. Justify the statement by citing examples from your location. Also built a production function based on your example. (MAY-2015)
Answer:
Production is possible only through effective utilisation of factors of production. The factors of production like land, labour, capital and organisation are called inputs. In the production process, these inputs. In the production process, these inputs are transformed into output. Thus a production function stands for functional relationship between inputs and output.
In my locality paddy is produced by combining inputs like labour, machinery, land, bank loan and organisers efforts. These are inputs. Thus the paddy production function can be stated as follows.
Q = f(X₁, X₂, X₃ ,X_n)
Where Q = paddy, X₁, X₂ ……… X_n are inputs used.

Question 24.
i) There is an error in the diagram. Redraw the diagram by correcting the same (MARCH-2016)

ii) Explain the relationship between Average Product (AP) & Marginal Product (MP)
Answer:
i)

ii) a) When MP is greater than AP, AP rises.
b) When MP is less than AP, AP falls.
c) When MP = AP, AP is at its maximum.

Question 25.
The relationship between input & Output is ______ (MARCH-2016)
Answer:
Production function

Question 26.

Draw the diagram correctly (MARCH-2016)
(AFC – Average Fixed Costs)
Answer:

Question 27.
 is _____  (MARCH-2016)
а) MC
b) AC
c) FC
d) VC
[TC = Total Cost, q = Output, MC = Marginal Cost, AC = Average Cost, FC = Fixed Cost, VC = Variable Cost]
Answer:
a) MC

Question 28.
State and explain the ‘law of variable proportions’ (MAY-2016)
Answer:
When more and more units of a variable input are added with the fixed input, the marginal product would increase only upto a certain point. Thereafter, the marginal product declines. This phenomenon is known as the Law of Variable Proportions. It is also known as returns to a factor.
The shape of TP, AP and MP suggests that they are specifically passing through three phases.
They are:
First phase : In the first stage, both AP and MP increase. As a result TP also increases at an in-creasing rate. This stage is known as the stage of increasing return to a factor. AP reaches the maximum level in this stage.
Second phase : Both AP and MP decrease at this stage. The TP increases at a decreasing rate. More importantly, TP reaches maximum and MP touches zero. This stage is also known as the stage of diminishing returns to a factor.
Third phase : At this stage, the MP becomes negative. As a result, TP also starts declining. The decline of AP is continuous. In the graph, when TP reaches maximum and MP touches zero. When MP becomes negative, TP starts declining. This stage is known as the stage of negative returns to a factor.

Question 29.
The cost curve which is a rectangular hyperbola is (MAY-2016)
a) ATC
b) AFC
c) TFC
d) AVC
Answer:
b) AFC

Question 30.
Short run marginal cost curve cuts average variable cost curve from below at the (MAY-2016)
a) the minimum point of AVC
b) any point of AVC
c) the falling portion of AVC
d) the rising portion of AVC
Answer:
a) the minimum point of AVC

Question 31.
Match the following: (MARCH-2017)

Answer:

Question 32.
Rising portion of long run marginal cost curve from the minimum of long run average cost curve is known as (MARCH-2017)
a) Long run supply curve of the firm.
b) Long run demand curve of the firm.
c) Variable cost curve of the firm.
d) Fixed cost curve of the firm.
Answer:
Long run supply curve of the firm.

Question 33.
The following table shows the total cost schedule of a firm. Calculate TVC, AFC, AVC, SAC and SMC schedules. (MARCH-2017)

TVC = Total Variable Cost, AFC = Average Fixed Cost, AVC = Average Variable Cost, SAC = Short run Average Cost, SMC = Short run Marginal cost)
Answer:

Kerala State Board New Syllabus Plus Two Economics Chapter Wise Previous Questions and Answers Part I Chapter 2 Theory of Consumer Behaviour.

Kerala Plus Two Microeconomics Chapter Wise Previous Questions Chapter 2 Theory of Consumer Behaviour

Question 1.
The demand function of commodity X of three Households are given below: (MARCH-2008)
Household 1 – D_x = 50 – 5 P_x
Household 2 – D_x = 50 – 6 P_x
Household 3 – D_x = 50 – 3 P_x
If the values of P_x are (5,4, 3, 2,1)
a) Prepare the Household demand schedule.
b) Calculate the market demand schedule.
c) Draw the three Household demand curves on the same axis.
Answer:
a)

Question 2.
State whether the following statements are true or false. Justify your answer. (MARCH-2009)
a) Equilibrium price is the price at which the demand for the commodity is greater than its supply.
b) A rise in supply due to non-price factors is called
expansion in supply.
Answer:
a) False.
Equillibrium price is the price at which the demand for the commodity is equal to supply.
b) False.
Increase in supply.

Question 3.
Sree Ram buys 10kg of wheat at a price of ₹ 20 per kg. It is found that the price elasticity of demand is 2. At what price he will be ready to buy 15 kg. of wheat? Exhibit in a diagram. (MARCH-2009)
Answer:

Question 4.
The Demand function of Commodity ‘y’ of two households are given below: (MARCH-2009)
Household I: DY = 80 – 20P Household II: DY= 100 – 20P If the value of P_y are 1,2, 3,4, 5
a) Derive the demand schedule of two households.
b) Draw the two household demand curves on the
same axis.
Answer:
Demand Schedule of Household I

Demand Schedule of Household II

Question 5.
A seller supplies 100 Kg. of rice at price ₹25. It is found that price elasticity of supply is 2. At what price he will be ready to sell 150 Kg. of rice?
(MAY-2009)
Answer:
Price elasticity of supply is defined as the degree of responsiveness of change in supply due to change in price. That is,
–
Therefore, new price = 25 + 6.25 = 31.25

Question 6.
The demand function of commodity x for three households are given below: (MAY-2009)
D_x= 300-30 P_x (1)
D_x = 200 – 20 P_x (2)
D_x= 200 – 10 P_x (3)
If the value of Px are 5, 4, 3,2 and 1.
a) Prepare the individual demand schedule.
b) Prepare the market demand schedule.
c) Draw the market demand curve.
Answer:
a) There are Three individual demand schedules.

Question 7.
Calculate the elasticity of demand by using total expenditure method from the data given below: (MAY-2009)

Answer:

Change in price leading to changes in quantity demanded causes changes in total expenditure incurred on commodity. By looking at the variation in total expenditure, price elasticity can be calculated. Since total expenditure remaining the same when price changes, elasticity is equal to one (unitary elastic demand).

Question 8.
During Onam festival Govt, of Kerala offered 20% discount on the prices of Khadi items. As a result of this sales of Khadi items registered an increase of 30%. Find out price elasticity by applying appropriate method. (MAY-2009)
Answer:
Price elasticity of demand can be found out by using the formula

The method used here is percentage or proportional method.

Question 9.
What may happen to the supply of two wheelers if Tata introduces new car at low cost and supplies them in the market which is more or less equal to prices of two wheelers? (MAY-2009)
Answer:
When a new car is supplied in the market at a lower price, the demand for two wheelers will be reduced. This is because, more customers will switch over their demand of two wheelers and start demanding the new car.

Question 10.
The Govt, of Kerala decided to abolish lottery system from November2008 onwards. Do you agree with the policy of the Govt, of Kerala? Justify your answer. (MAY-2009)
Answer:
Yes/No
State any answer and substantiate the answer

Question 11.
A production possibility schedule for good x and y is given below: (MARCH-2010)

a) Define production possibility frontier.
b) Draw the PPC.
Answer:
a) A production possibility curve is a geometrical device representing all such combinations of two goods that can be produced with given technology and available resources,

Question 12.
A consumer purchased 4 kg. of good A when his income was ₹500 per month. He reduces the consumption of good A to 2 kg. when his income alone increase to ₹1,000 per month. If so, (MARCH-2010)
a) State the nature of good A and justify.
b) Give one example for commodity like good A.
Answer:
a) Inferior goods or Giffen goods
b) Bajra, Ragi, Tapioca, etc.

Question 13.
An indifference curve possesses several properties. One of them is that, it is a downward sloping curve from left to right. Write any other two properties. (MARCH-2010)
Answer:
a) Indifference curve is convex to origin
b) Higher and higher indifference curve represents higher level of satisfaction.
c) Indifference curves never intersect each other.

Question 14.
Observe the diagram (MARCH-2010)

a) Comment on the given demand curve.
b) Give any two reasons for the positional change of demand curve from D_d to D_p.
Answer:
a) Shift in demand / increase in demand
b) Increase in income of the consumers. Change in taste and preference of the consumers.

Question 15.
“The direction of change in equilibrium price and quantity is same whenever there is a shift in demand curve.” (MAY-2010)
a) Identify the two types of shift in demand curve.
b) Draw the relevant diagrams.
Answer:
a) Increase in demand and decrease in demand.
b)

Question 16.
Ramu has an income of ₹20 and suppose he wants to consume two commodities X and Y, both the goods are priced at ₹4 per unit. (MAY-2010)
a) Find out all the budget sets available to Ramu.
b) Draw the budget-line.
c) What factors can change the budget set of Ramu?
Answer:
a) 4x + 4y = 20

Question 17.
“Prices of related goods affect the household demand, and we can differentiate the related goods into two types.” (MAY-2010)
a) Which are the types of related goods that determine the demand?
b) Define them.
Answer:
) Substitutes
ii) Complementaries
b) Substitutes are those goods where one good can be used instead of other. Eg. Tea and Coffee. Complementary goods are those goods which are used together. Eg. Car and Petrol.

Question 18.

From the following indifference curve, mark (MARCH-2011)
a) monotonic preferences
b) inferior bundles
c) Preferred bundles
Answer:
a) D b) E c) D

Question 19.
Raghu, Yadav and Basheer are 3 customers who purchased mangoes from a market. Individual quantity demanded for mangoes are given in the schedule. (MARCH-2011)

a) Construct market demand schedule
b) Draw market demand curve.
c) Based on the given schedule, identify the nature of good (Hint: Normal, Inferior, Giffen).
Answer:

Question 20.
A consumer wants to consume two goods ‘x’ and ‘y’ with his income of ₹20. The prices of the two goods are ₹4 and ₹5 respectively.
a) Write down the equation of the budget line. (MARCH-2012)
b) Represent the budget line diagramatically.
c) How much of good x can the consumer consume if he spends his entire income on that good?
Answer:
a) 4x + 5y = 20

Question 21.
Consider the demand for a good. At a price ₹4 the demand for the good is 30 kg. Suppose price of the good increases to ₹5 and as a result the demand for the good falls to 20 kg. Calculate the price elasticity of demand. (MARCH-2012)
Answer:
Elasticity of demand

Question 22.
Consider the following figure: (MARCH-2012)
Why point E in the figure is considered as consumer’s optimum? Justify your answer.

Answer:
Point E is considered as consumers’s optimum. The optimum bundle of the consumer is located at the point where the budget line is tangent to one of the indifference curves. It is drawn below

Condition I : Budget line should be tangent to the indifference Curve
Condition II: Slope of IC ((MRS_xy)) should be equal to slope of budget line (Price Ratio)

Question 23.
In economics, it is generally assumed that consumer is rational. The consumer have well defined preference over a set of available bundle. He always tries to maximise his satisfaction or attain the optimum level. Diagrammatically illustrate the consumer’s optimum. (Hint: Consumer’s equilibrium). (MARCH-2013)
Answer:
Consumer’s Equilibrium
Consumer’s equilibrium shows a situation in which a consumer buys such a combination of goods from which he gets the maximum satisfaction with his given income and given prices of the goods.
The term consumer’s equilibrium refers to the amount of goods and services which the consumer may buy in the market given his income and given prices of goods in the market. The aim of the consumers is to get maximum satisfaction from his money income. Given the price line (budget line) and the indifference map, a consumer is said to be in equilibrium at a point where the price line is touching the highest attainable indifference curve from below. Thus the consumer’s equilibrium under the indifference curve theory must meet the following two conditions.
First order condition.
A given price line should be tangent to an indifference curve or marginal rate of substitution of good X for good Y (MRSxy) must be equal to the price ratio of the two goods.
(MRS_xy) = (P_x)/(P_y) Second order condition.
The second condition is that indifference curve must be convex to the origin at the point of tangency. Assumptions
The following assumptions are made to determine the consumer’s equilibrium position.
(1) Rationality. The consumer is rational. He wants to obtain maximum satisfaction given his income and prices.
(2) Utility is ordinal. It is assumed that the consumer can rank his preferences according to the satisfaction of each combination of goods.
(3) Consistency of choice. It is also assumed that the consumer is consistent in the choice of goods.
(4) Perfect competition. There is perfect competition in the market from where the consumer is purchasing the goods.
The optimum bundle of the consumer is located at the point where the budget line is tangent to one of the indifference curves. It is drawn below.

Condition I: Budget line should be tangent to the in-difference Curve
Condition II: Slope of IC ((MRS_xy)) should be equal to slope of budget line (Price Ratio)

Question 24.
Identify the relationship between good X and good Y. (MAY-2014)
i) Price of good X rises and demand for good Y rises, goods are
ii) Price of good X falls and demand for good Y rises, goods are
Answer:
i) Substitutes
ii) Complementary goods

Question 25.
Let Price of good X((P_x)) = ₹3 price of good Y((P_x)) = ₹5, income of the consumer (Y) = 130 and assume whole income is spend on good X and good Y. (MAY-2014)
a) Construct the budget equation and draw the budget line.
b) Suppose the prices of both goods, X and Y doubles, then what happens to the budget equation and the budget line?
c) Suppose income of the consumer (Y) doubles, then what happens to the budget equation and the budget line?
Answer:
a)

b) budget equation becomes 6X + 10 Y = 30 budget line will shift downward by half
c) budget equation becomes 3X+ 5 Y = 60 budget line will shift outward

Question 26.
Calculate the. price elasticity of demand from a movement from point A to B on the demand curve DD. (MAY-2014)

Answer:

Elasticity is 2.5. (Elastic demand)

Question 27.
If the demand curve is a rectangular hyperbola, elasticity is (MARCH-2015)
a) zero b) One
c) Less than one d) Infinity
Answer:
b) One

Question 28.
Mr. Abhi wants to consume two goods. The prices of two goods are ₹4 and ₹5 respectively. If Abhi’s income is ₹20, answer the following questions: (MARCH-2015)
a) Write down the equation of the budget line.
b) How much of good-1 that Abhi can consume if he spends his entire income on good-1?
c) How much of good-2 that Abhi can consume if he spends his entire income on good-2?
d) ‘ What is the slope of budget line?
e) How does the budget line change if the customer’s income increases from ₹20 to ₹40 but prices remain unchanged?
f) Show the change in budget line if the price is
good – 2 decreases by ₹1 but the price of good – 1 and consumers income remains unchanged.
Answer:

e) When income of the consumer increases without any changes in the price then the budget line shifts parallel upwards to the earlier budget line.

When only the price of good 2 decreases the budget line changes upwards in the good 2 axis, (vertical intercept)

Question 29.
“Consumer’s optimum bundle is located at the point of tangency between the budget indifference curve.” Explain with the help of a suitable diagram. Hint: Indifference Curve Analysis (MAY-2015)
Answer:
Consumer’s Equilibrium Consumer’s equilibrium shows a situation in which a consumer buys such a combination of goods from which he gets the maximum satisfaction with his given income and given prices of the goods.
The term consumer’s equilibrium refers to the amount of goods and services which the consumer may buy in the market given his income and given prices of goods in the market. The aim of the consumers is to get maximum satisfaction from his money income. Given the price line (budget line) and the indifference map, a consumer is said to be in equilibrium at a point where the price line is touching the highest attainable indifference curve from below. Thus the consumer’s equilibrium under the indifference curve theory must meet the following two conditions.
The following assumptions are made to determine the consumer’s equilibrium position.
1) Rationality. The consumer is rational. He wants to obtain maximum satisfaction given his income and prices.
2) Utility is ordinal. It is assumed that the consumer can rank his preferences according to the satisfaction of each combination of goods.
3) Consistency of choice. It is also assumed that the consumer is consistent in the choice of goods.
4) Perfect competition. There is perfect competition in the market from where the consumer is purchasing the goods.
The optimum bundle of the consumer is located at the point where the budget line is tangent to one of the indifference curves. It is drawn below.

Condition I: Budget line should be tangent to the indifference Curve
Condition II: Slope of IC (MRS_xy) should be equal to slope of budget line (Price Ratio)

Question 30.
Suppose there was a decrease in the price of good ‘X’ and as a result, the demand for good ‘Y’ increases. What will be the type of goods? (MAY-2015)
Answer:
Complementary goods.

Question 31.
Consider the demand curve D = 10 – 3p. What is the elasticity of price \(\frac { 5 }{ 3 }\) (MAY-2015)
Answer:

Elasticity is = 3

Question 32.
P₁ X₁+P₂ X₂ ≤ M is a budget constraint. Identify the constraints. (MARCH-2016)
Answer:
P₁, P₂, M

Question 33.
Given the diagram (MARCH-2016)

a) Identify:
i) AB
ii) Pont E
b) Elaborate the properties of indifference curve.
c) Point ‘C’ is not the equilibrium of the consumer,
do you agree? Explain.

Answer:
a) i) AB is the Budget line
ii) Point E is the equilibrium point
b) Properties of indifference curves are:
Indifferences curves are negatively sloped.
Indifference curves are convex to origin.
Higher and higher indifference curve represents higher level of satisfaction.
Two indifference curves never intersect each other.
c) I agree. Equilibrium point is reached by satisfying the following conductions.
1) IC must be tangent with budget line.
2) Slope of IC must be equal to slope of budget line.
These two conditions are satisfied at the point E. Hence ‘C’ is not the equilibrium point.

Question 34.
Distinguish between the movement along a demand . curve and the shifts in demand curve. (MAY-2016)
Answer:
Change in quantity demanded due to change in price leads to expansion and contraction of demand. In this case, there is the movement along a demand curve.
Change in quantity demanded due to change in factors other than price leads to increase and decrease in demand. In this case, there is shift in demand curve.

Question 35.
“The consumer’s optimum bundle is located at the point of tangency between the budget line and the highest indifference curve”. Explain the consumers’ equilibrium as per the indifference curve approach with a suitable diagram. (MAY-2016)
Answer:
The interest of the consumer is to purchase those goods and services which provides him maximum satisfaction. So the consumer chooses the best bundle available to him. The consumer always prefers to have bundles on the higher indifference curve. The preference of the consumer to have the bundle, which provides him maximum satisfaction, is known as consumer’s equilibrium. It is the optimum point, a point of maximum satisfaction.
The equilibrium of the consumers is possible only when the budget line is tangent to the indifference curve. The consumer purchases the goods and services on the budget line, which provides him maximum satisfaction. It is possible only when the slope of the budget line  and the slope of the indifference curve (MRS) are equal.

Question 36.
Why there is different price elasticity along a linear demand curve? Illustrate with the help of a diagram. (MARCH-2017)
Answer:
The price elasticity of a linear demand curve is based on slope of demand curve. Slope of the demand curve is the ratio between change in quantity demanded (∆q) to change in price (∆p). So the slope of a demand curve will be different at different points. This can be explained with diagram.

Question 37.
From the Budget line shown below, find the price of good X₂ given that the price of X₁ good is ? 30. The equation on the Budget line is given as P₁X₁+ P₂ X₂=1000 (MARCH-2017)

Answer:

Kerala State Board New Syllabus Plus Two Computer Application Notes Chapter 5 Web Designing Using HTML.

Kerala Plus Two Computer Application Notes Chapter 5 Web Designing Using HTML

3 types of Lists in HTML.

1. Unordered List (<UL>) – Items are displayed with square, circle or disc in front.

2. Ordered List (<OL>) – Items are displayed with the following type values.

• Type = 1 for 1,2, 3, ……..
• Type = i for i, ii, iii, ………
• Type = I for I, II, III, ……….
• Type = a for a, b, c, ………..
• Type = A for A, B, C, …………

3. Definition List (<DL>) – It is formed by definitions.
<L/> – It is used to specify List items.
<DT> – It is used to specify Definition Term.
<DD> – Used to specify the description
<A> is used to provide hyperlinks. Two types of linking. Its attribute is HREF.

1. External link – Used to connect 2 different web pages.
2. Internal link – Used to connect different locations of same page.

Concept of URL
URL means Uniform Resource Locator.
Two types of URL
a) Relative URL – Here we explicitly give the web site address
Eg: <A href=http://www.hscap.kerala.gov.in>

b) Absolute URL – Here we implicitly give the website address. The path is not specified here.
Eg: Consider the web pages index.html and school.html saved in the folder C:\BVM.
The file indexs.html contains the following.
<A href=”school.html”>.

Here we did not specify the full path of the file school.html. But this implicitly points to the file stored in C:\BVM

Creating Graphical hyperlinks
It can be achieved by using the <img> tag inside the <a> tag.
Eg: <A href=”school.html”><img src=”schoo|.jpg”></A>

Creating E- mail linking
It can be achieved by using the key word mailto as a value to href attribute
Eg: <A href=mailto:”info@spark.gov.in”> SPARK</A>

Insert music and videos
<embed> tag is used to add music or video to the page

Attributes

• src – specifies the file to play
• width – Specifies the width of the player
• height – Specifies the height of the player
• hidden – Used to specifies the player is visible or not
• <noembed> – Used to specifies an alternate when the browser does not support the <embed> tag.

Attribute

• src – Used to specify the image file
• alt – Used to specify the alternate text

Eg:
<html>
<head>
</head>
<body>
Here is a tag embed to play music
<embed src=”c:\alvis.wma” width=”500″ height=”500″ hidden=”true”> </embed>
</body>
</html>

<bgsound> tag
This tag is used to play back ground song or music
Eg:
<html>
<head>
</head>
<body>
<bgsound src=”c:\alvis.wma” loop=”infinite”>
</body>
</html>

• <Table> is used to create a table.
• <TR> is used to create a row.
• <TH> is used to create heading cells.
• <TD> is used to create data cells.

<Table> Attributes

1. Border – It specifies the thickness of the borderlines.
2. Bordercolor – Color for borderlines.
3. Align – Specifies the table alignment in the window.
4. Bgcolor – Specifies background colour.
5. Cellspacing – Specifies space between table cells.
6. Cellpadding – Specifies space between cell border and content.
7. Cols – Specifies the number of columns in the table.
8. Width – Specifies the table width.
9. Frame – Specifies the border lines around the table.
10. Rules – Specifies the rules (lines) and it overrides the border attribute. Values are given below:
    • none – display no rules
    • cols – display rules between columns only(vertical lines)
    • rows – display rules between rows only(horizontal lines)
    • groups – display rules between row group and column groups only
    • all – rules between all rows and columns

<TR> attributes

1. align – specifies the horizontal alignment. Its val¬ues are left, right, centre or justify.
2. Valign – Specifies the vertical alignment. Its values are top, middle, bottom or baseline.
3. Bgcolor – Used to set background-color

<TH> and <TD> attributes

1. Align – specifies a horizontal alignment. Its values are left, right, centre or justify.
2. Valign – Specifies vertical alignment. Its values are top, middle, bottom or baseline.
3. Bgcolor – Specifies border color for the cell.
4. Colspan – Specifiesthenumberofcolumnsspan for the cell.
5. Rowspan – Specifies the number of rows span for the cell.

Frameset – It is used to divide the window into more than one pane. It has no body section.

<Frameset> attributes

1. cols – It is used to divide the window vertically.
2. rows – It is used to divide the window horizontally.
3. border – specifies the thickness of the frame border.
4. bordercolor – specifies the color of the frame border.

Frame – It specifies the pages within a frameset.

<Frame> attributes

1. SRC – specifies the web page.
2. Scrolling – Scroll bar is needed or not its values are yes, no or auto.
3. Noresize – It stops the resizing of the frame.
4. Margin width and Marginheight – Sets margins
5. Name – To give a name for the frame.
6. Target – specifies the target.

<Noframe> – It is used to give content when some browsers that do not support frameset.
Nesting of framesets
Step 6: Finally execute the frame.html file

<Form> – It is used to take data from the users and send to the server.

<Input> – It is used to create input controls. Its type attribute determines the control type.

Main values of the type attribute are given below.

1. Text – To create a text box.
2. Password – To create a password text box.
3. Checkbox – Tq^teate a check box.
4. Radio – To create a radio button.
5. Reset – To create a Reset button.
6. Submit-To creates a submit button.
7. Button – To create a button

To create a group of radio buttons, then the name attribute must be the same.

<Textarea> is used to create a multiline text box. <Label> It is used to give labels.

<Select> It is used to create a list box or combo box. The items must be given by using <option> tag.

Attribute

Name – Specifies the name of the object to identify

Size – If it is 1, the object is a combo box otherwise it is a list box.

Multiple – Allows selecting multiple items

<Form> attributes

1) Action – Here we give the name of the program (including the path) stored in the Webserver.
2) Method – There are 2 types of methods get and post.

3) Target – Specifies the target window for displaying the result. Values are given below.

• _blank – Opens in a new window
• _self – Opens in the same frame
• _parent – Opens in the parent frameset
• _top – Opens in the main browser window
• name – Opens in the window with the specified name.
• <Fieldset> tag

This tag is helpful to divide a form into different subsections and form groups. <legend> tag used to give a caption forthe <fieldset> section.

Kerala State Board New Syllabus Plus Two Computer Application Notes Chapter 4 Web Technology.

Kerala Plus Two Computer Application Notes Chapter 4 Web Technology

Website – It is a collection of web pages contained text and multimedia(image, audio, video, graphics, animation etc) files.

A webpage is created by HTML tags

The first web page of a website is known as the home page.

www – means world wide web.

Portals – Rediff, Hotmail, Yahoo, etc are called portals from which the user can do multiple activities.

Communication on the Web
Following are the steps that happened in between the user’s click and the page being displayed

1. The browser determines the URL selected.
2. The browser asks the DNS for URLS corresponding IP address (Numeric address)
3. The DNS returns the address to the browser.
4. The browser makes a TCP connection using the IP address.
5. then it sends a GET request for the required file to the server.
6. The server collects the file and sends it back to the browser.
7. The TCP connection is released.
8. The text and the images in the web pages are displayed in the browser.

Client to Web Server Communication
This communication is carried out between the client to the webserver (shopping site). The technology used to protect data that are transferred from client to web server is HTTPS (HyperText Transfer Protocol Secure). This encrypts user name, password etc., and sent to the server. HTTPS works using Secure Sockets Layer (SSL) ensures privacy as well as prevents it from unauthorized access (changes) from other websites. Following are the steps

1. The browser requests a web page to the server.
2. The server returns its SSL certificate.
3. The browser checks the genuinity of the certificate by the authorised certification authority
   (Eg: Veri sign)
4. The certificate authority certifies whether it is valid or not.
5. If it is valid the browser encrypts the data and transmits it. The certificate can be viewed by click on the lock symbol.

Web Server to Web Server Communication
This communication is usually carried out between web server (seller) to another web server (normally bank). For the safe transactions Digital certificate issued by third party web sites are used.
Payment gateway is a server (Computer) that acts as a bridge (interface) between merchant’s server and bank’s server to transfer money.

Web Server Technologies

Web server: A computer with high storage capacity, high speed and processing capabilities is called a web server.

Software ports: The computer is not a single unit. It consists of many components. The components are connected to the computer through various ports. Two types of ports Hardware and Software.

Hardware ports: Monitors are connected through VGA ports and the keyboard or mouse are connected through PS/2 ports.

Software ports: It is used to connect client computers to servers to access different types of services. For example HTTP, FTP, SMTP etc. Unique numbers are assigned to software ports to identify them. It is a 16-bit number followed by an IP address.

DNS Servers
A DNS server is a powerful computer with networking software. It consists of domain names and their corresponding IP addresses. A string address is used to represent a website, it is familiar to humans. The string address is mapped back to the numeric address using a Domain Name System (DNS). It may consist of 3 or 4 parts. The first part is www., the second part is the website name, the third top-level domain, and the fourth geographical top-level domain.
eg.- http://www.nic.kerala.gov.in / results.html.

http – http means hypertext transfer protocol. It is a protocol used to transfer hypertext.
www – World Wide Web. With an email address, we can open our mailbox from anywhere in the world.
nic.kerala – It is a unique name. It is the official website name of the National Informatics Centre.
<script> in – It is the geographical top-level domain. It represents the country, in is used for India.
results.html – It represents the file name.

Web Designing
Any text editor can be used for web designing. Besides that many software tools are available in the market to make the web pages more attractive and interactive, some of the popular softwares are Adobe dream weaver, Microsoft Expression web, Blue fish, Bootstrap etc.

Static and Dynamic Web Pages
Some pages are displaying same content(same text, images,etc) every time. Its content are not changing. This type of web pages are called static page. Conventional wep pages display static pages and has some limitations.
Advanced tools are used to create web pages dynamic, which means pages are more attractive and interactive. For this JavaScript, VBScript, ASP, JSP, PHP, etc are used.
Following are the differences

Scripts
Scripts are small programs embedded in the HTML pages.
<script> tag is used to write scripts The attributes used are
Type – To specify the scripting language
Src – Specify the source file

Two types of scripts
1. Client scripts – These are scripts executed by the browser.
Eg: VB Script, Javascript etc.
2. Server scripts – These are scripts executed by the server.
Eg: ASP, JSP, PHP, Perl, etc.

The languages that are used to write scripts are known as scripting languages.

Scripting Languages
a. JavaScript: Java script(developed by Brendan Eich for the Netscape browser) is a platform independent scripting language. Means It does not require a particular browser. That is it runs on any browser hence it is mostly accepted scripting language.
Ajax: It is a technology to take data from the server and filled in the text boxes without refreshing (without reloading the entire page) the web page. Ajax is Asynchronous JavaScript and Extensible Mark up Language (XML). XML is an Extensible Mark up Language, it allows to create our own new tags. This technology uses JavaScript to perform this function. When we turned off JavaScript features in the browser, the Ajax application will not work.

b. VB Script: VB Script(developed by Microsoft) is a platform dependent scripting language. Means it requires a particular browser(MS Internet Explorer) to work that is’why it is not widely accepted scripting language.

c. PHP (PHP Hypertext Preprocessor)

• It is an open source, general purpose scripting language.
• It is a server side scripting language
• Introduced by Rasmus Lendorf
• A PHP file with extension .php
• It supports data base programming the default DBMS is MySQL
• It is platform independent
• PHP interpreter in Linux is LAMP(Linux, Apache, MySQL, PHP)

d. Active Server Pages (ASP)

• ASP introduced by Microsoft
• ASP stands for Active Server Page.
• ASP’s are web pages that are embedded with dynamic contents, such as text, HTML tags and scripts.
• An ASP file uses .asp extension.
• In ASP, the script executes in the server and the effect will be sent back to the client computer.
• Here a real time communication exists between the client and server.
• ASP applications are very small.
• The only server used is Microsoft Internet Information Server(IIS), hence it is platform dependant

e. Java Server Pages (JSP)

• JSP introduced by Sun Micro System
• JSP stands for Java Server Page.
• An JSP file uses .jsp extension
• It is platform-independent
• It uses Apache Tomcat webserver
• JSP binds with Servlets (Servlets are Java codes run in Server to serve the client requests).

Cascading Style Sheet (CSS)
It is a style sheet language used for specifying common format like colour of the text, font, size, etc. other than the HML codes. That is CSS file used to separate HTML content from its style.
It can be written in 3 ways as follows:

1. Inline CSSIn the body section of the HTML file
2. Embedded CSS In the head section of the HTML file
3. Linked CSS A separate file(extemal file, eg. bvm.css) with extension .css and can be linked in the web page

Code reusability(just like a function in C++) is the main advantage of CSS and can be used in all the pages in a website

• HTML – Hyper Text Markup Language. Used to create webpage.
• A website is a collection of web pages.
• It was developed by Tim Berners – Lee in 1980 at CERN.
• Lynx, a text only browser for unix.
• Mosaic it is a graphical browser.
• Netscape’ Navigator, Microsoft Internet Explorer, Opera, Ice Weasel,Mozilla FireFox etc. are dif¬ferent browsers.
• Java, C#are programming languages used for web applications.
• HTML files are saved with .htm or .html.
• A web browser is a piece of software used to view web pages.

Structure of an HTML Document

<HTML>
<HEAD>
<TITLE>
give title to the web page here
</TITLE>
</HEAD>
<BODY>
This is the body section.
</BODY>
</HTML>

Tags are keywords used to define the HTML document. Two types of tags Empty and container. The container tag has both an opening and closing tags. But empty tag has an opening tag only, no closing tag.
Eg: empty tag: <hr>, <br> etc.
container tag: <html>, </html>, etc.

Attributes are parameters used for providing additional information within a tag.

An HTML document has 2 sections. Head section and body section.

Attributes of <HTML> tag
1. Dir – This attribute specifies the direction of text displayed on the webpage, values are ltr(left to right), rtl(right to left)
2. Lang – This attribute specifies the language values are En(English), Hi(Hindi), Ar(Arabic), etc
Eg: <HTML dir=”ltr” lang=”Hi”>

The title tag is given in the head section.

Web page contents are given in the body section.

Attributes of the Body tag.
Bgcolor, Background, Text, Link, ALink, VLink, LeftMargin andTopmargin

Heading Tags(6 tags)
<H1 >,<H2>,<H3>,<H4>,<H5> and <H6>.

<H1> provides big heading and <H6> provides smallest

<HR> is used to draw a horizontal line. Its attributes are size, width, no shade and color.

<BR> is used to break a line.

Six Heading tags are used in HTML <H1 > to <H6>.

<B> to make the content Bold.

<I> to make the content in Italics.

<U> to underline the content.

<S> and <STRIKE> – These two are used for striking out the text

<BIG> To make the text size bigger than the normal text

<SMALL> To make the size smaller than the normal text.

<STRONG> The effect is same as <B> tag. That is to emphasize a block of text

<EM> – The effect is same as <i> tag

<SUB> – create a subscript

<SUP> create a superscript

<BLOCKQUOTE> – It is used to give indentation(giving leading space to a line)

<Q> It is used to give text within double quotes

<PRE> (Preformatted text) – This tag is used to display the content as we entered in the text editor.

<ADDRESS> This tag is used to provide information of the author or owner.

<MARQUEE> – This tag is used to scroll a text or image vertically or horizontally.

Attributes of <MARQUEE>

Height – Sets the height of the Marquee text

Width – Sets the width of the Marquee text

Direction – Specifies the scrolling direction of the text such as up, down, left or right

Behavior- Specifies the type such as Scroll, Slide(Scroll and stop)and altemate(to and fro).
<marquee behavior=”scroirscrollamount=”100″> hello</marquee>
<manquee behavior=”slide” scrollamount=”100″> hello</manquee>
<marquee behavior=”alternate” scrollamount= “100”>hello</manquee>

Scrolldelay – Specifies the time delay in seconds between each jump.

scrollamount- Specifies the speed of the text

loop – This specifies the number of times the marquee scroll. Default infinite.

bgcolor – Specifies the back ground colour.

Hspace – Specifies horizontal space around the marquee

Vspace – Specifies vertical space around the marquee

<Div> – Used to define a section or a block of text with the same format.

Attributes
align – Sets the horizontal alignment. Values are left, right, center and justify
Id – Used to give a unique name
Style – Specify a common style to the content for example
<Font> used to specify the font characteristics. Its attributes are size, face, and color.

Special Characters

<IMG> tag is used to insert an image. Its important attributes are align, height, width and alt.

Comments are given by using <!– and → symbols.

Kerala State Board New Syllabus Plus Two Computer Application Notes Chapter 3 Functions.

Kerala Plus Two Computer Application Notes Chapter 3 Functions

String handling using arrays: A string is a combination of characters hence char data type is used to store the string. A string should be enclosed in double-quotes. In C++ a variable is to be declared before it is used.Eg. “BVM HSS KALPARAMBU”.

Memory allocation for strings: To store “BVM” an array of char type is used. We have to specify the size. Remember each and every string is end with a null (\0) character. So we can store only size-1 characters in a variable. Please note that \0 is treated as a single character. \0 is also called as the delimiter, char school_name[4]; By this, we can store a maximum of three characters.

Consider the following declarations
char my_name[10]=”Andrea”;
char my_name2[]=”Andrea”;
char str[ ]=”Hello World”

In the first declaration 10 Bytes will be allocated but it will use only 6+1 (one for ‘\0’) = 7 Bytes the remaining 3 Bytes will be unused. But in the second declaration the size of the array is not mentioned so only 7 Bytes will be allocated and used hence no wastage of memory. Similarly in the third declaration the size of the array is also not mentioned so only 12( one Byte for space and one Byte for‘\0’) Bytes will be allocated and used hence no wastage of memory.

Input / output operations on strings

Consider the following code

# include<iostream>
using namespace std;
int main()
{
charname[20];
cout<<“Enter your name:”; cin>>name;
cout<<“Hello “<<name;
}

If you run the program you will get the prompt as follows:
Enter your name: Alvis Emerin
The output will be displayed as follows and the “Emerin” will be truncated.
Hello Alvis

This is because of cin statement that will take upto space. Here space is the delimiter. To resolve this gets() function can be used. To use gets() and puts() function the header file stdio.h must be included. gets() function is used to get a string from the keyboard including spaces.
puts() function is used to print a string on the screen. Consider the following code snippet that will take the input including the space.

# include<iostream>
#include<cstdio>
using namespace std;
int main()
{
charname[20];
cout<<“Enter your name:”;
gets(name);
cout<<“Hello”<<name;
}

More console functions
Input functions

Output functions

Stream functions for I/O operations: Some functions that are available in the header file iostream.h to perform I/O operations on character and strings(stream of characters). It transfers streams of bytes between memory and objects. Keyboard and monitor are considered as the objects in C++.

Input functions: The input functions like get( ) (to read a character from the keyboard) and getline() (to read a line of characters from the keyboard) is used with cin and dot(.) operator.

Eg.

# include<iostream>
using namespace std;
int main()
{
char str[80], ch= 'z';
cout<<“enter a string that end with z:”;
cin.getline(str, 80, ch);
cout<<str;
}

If you run the program you will get the prompt as follows:
Enter a string that end with z: Hi I am Jobi. I am a teacherz. My school is BVM HSS
The output will be displayed as follows and the string after ‘z’ will be truncated.
Hi I am Jobi. I am a teacher

Output function: The output functions like put() (to print a character on the screen) and write() (to print a line of characters on the screen) is used with cout and dot(.) operator.

Complex programs are divided into smaller subprograms. These subprograms are called functions.
Eg. main(), clrscr(), sqrt(), strlen(),…

Concept of modular programming: The process of converting big and complex programs into smaller programs is known as modularisation. These small programs are called modules or subprograms or functions. C++ supports modularity in programming called functions.

Merits of modular programming

• It reduces the size of the program
• Less chance of error occurrence
• Reduces programming complexity
• Improves reusability

Demerits of modular programming
While dividing the program into smaller ones extra care should be taken otherwise the ultimate result will not be right.

Functions in C++
Some functions that are already available in C++ are called pre defined or built in functions.
In C++, we can create our own functions for a specific job or task, such functions are called user-defined functions.
A C++ program must contain a mainO function. A C++ program may contain many lines of statements(including so many functions) but the execution of the program starts and ends with main() function.

Predefined functions
To invoke a function that requires some data for performing the task, such data is called parameter or argument. Some functions return some value back to the called function.

String functions
To manipulate string in C++ a header file called string.h must be included.
a) strlen() – to find the number of characters in a string(i.e. string length).
Syntax: strlen(string);
Eg.
cout<<strlen(“Computer”); It prints 8.

b) strcpy() – It is used to copy the second string into the first string.
Syntax: strcpy(string1, string2);
Eg.
strcpy(str, “BVM HSS”);
cout<<str; It prints BVM HSS.

c) strcat() – It is used to concatenate the second string into first one.
Syntax: strcat(string1, string2)
Eg.
strcpy(str1, “Hello”);
strcpy(str2, “World”);
strcat(str1, str2);
cout<<str1; It displays the concatenated string “Hello World”

d) strcmp() – it is used to compare two strings and returns an integer.
Syntax: strcmp(string1, string2)

• if it is 0 both strings are equal.
• if it is greater than 0(i.e. +ve) stringl is greater than string2
• if it is less than 0(i.e. -ve) string2 is greater than string1

Eg.

#include<iostream>
#include<cstring>
using namespace std;
int main()
{
char str1[10], str2[10];
strcpy(str1, “Kiran”);
strcpy(str2, “Jobi”);
cout<<strcmp(str1, str2);
}

It returns a +ve integer.

e) strcmpi() – It is same as strcmp() but it is not case sensitive. That means uppercase and lowercase are treated as same.
Eg. “ANDREA” and “Andrea” and “andrea” these are same.

#include<iostream>
#include<cstring>
using namespace std;
int main()
{
char str1[10], str2[10];
strcpy(str1, "Kiran”);
strcpy(str2, "KIRAN”);
cout<<strcmpi(str1, str2);
}

It returns 0. That is both are the same.

Mathematical functions.
To use mathematical functions a header file called math.h must be included
a) abs() – To find the absolute value of an integer.
Eg. cout<<abs(-25); prints 25.
cout<<abs(+25); prints 25.

b) sqrt() – To find the square root of a number.
Eg. cout<<sqrt(49); prints 7.

c) pow() – To find the power of a number.
Syntax. pow(number1, number2)
Eg. cout<<pow(2, 10); It is equivalent to 210. It prints 1024.

Character functions
To manipulate the character in C++ a header file called ctype.h must be included.
a) isupper() – To check whether a character is in uppercase or not. If the character is in uppercase it returns a value 1 otherwise it returns 0.
Syntax: isupper(char ch);

b) islower() – To check whether a character is in lowercase or not. If the character is in lowercase it returns a value 1 otherwise it returns 0.
Syntax: islower(char ch);

c) isalpha() – To check whether a character is an alphabet or not. If the character is an alphabet it returns a value 1 otherwise it returns 0.
Syntax: isalpha(char ch);

d) isdigit() – To check whether a character is a digit or not. If the character is a digit it returns a value 1 otherwise it returns 0.
Syntax: isdigit(char ch);

e) isalnum() – To check whether a character is an alphanumeric or not. If the character is an alphanumeric it returns a value 1 otherwise it returns 0.
Syntax: isalnum(char ch);

f) toupper() – It is used to convert the given character into uppercase.
Syntax: toupper(char ch);

g) tolower() – It is used to convert the given character into lowercase.
Syntax: tolower(char ch);

User defined functions

Syntax:

Return type Function_name(parameter list)
{
Body of the function
}

1. Return type: It is the data type of the value returned by the function to the called function;
2. Function name: A name given by the user.

Different types of User-defined functions.

1. A function with arguments and return type.
2. A function with arguments and no return type.
3. A function with no arguments and with the return type.
4. A function with no arguments and no return type.

Prototype of functions

Consider the following codes

Method 1

# include<iostream>
using namespace std;
int sum(int n1, int n2)
{
return(n1+n2);
}
int main()
{
int n1, n2;
cout<<“Enter 2 numbers:”; cin>>n1>>n2;
cout<<“The sum is “<<sum(n1, n2);
}

Method 2

#include<iostream>
using namespace std;
int main()
{
int n1, n2;
cout<<“Enter 2 numbers:”; cin>>n1>>n2;
cout<<“The sum is “<<sum(n1, n2);
}
int sum(int n1, int n2)
{
retum(n1+n2);
}

In method 1 the function is defined before the main function. So there is no error.
In method 2 the function is defined after the main function and there is an error called “function sum should have a prototype”. This is because the function is defined after the main function. To resolve this a prototype should be declared inside the main function as follows.

Method 2

# include<iostream>
using namespace std;
int main()
{
int n1, n2;
int sum(int, int);
cout<<“Errter 2 numbers:"; cin>>n1>>n2;
cout<<“The sum is “<<sum(n1, n2);
}
int sum(int n1, int n2)
{
return(n1+n2);
}

Functions with default arguments
We can give default values as arguments while declaring a function. While calling a function the user doesn’t give a value as arguments the default value will be taken. That is we can call a function with or without giving values to the default arguments.

Methods of calling functions: Two types call by value and call by reference.
1. Call by value: In the call by value method, the copy of the original value is passed to the function, if the function makes any change will not affect the original value.
2. Call by reference: In the call by reference method, the address of the original value is passed to the function, if the function makes any change will affect the original value.

Scope and life of variables and functions
a) Local scope – A variable declared inside a block can be used only in the block. It cannot be used in any other block.
Eg.

#include<iostream>
using namespace std;
int sum(int n1, int n2)
{
int s;
s=n1+n2;
return(s);
}
int main()
{
int n1, n2;
cout<<“Enter 2 numbers:"; cin>>n1>>n2;
cout<<“The sum is “<<sum(n1, n2);
}

Here the variable s is declared inside the function sum and has a local scope;

b) Global scope – A variable declared outside of all blocks can be used anywhere in the program.

# include<iostream>
using namespace std;
int s;
int sum(int n1, int n2)
{
s=n1+n2;
return(s);
}
int main()
{
int n1, n2;
cout<<“Enter 2 numbers:"; cin>>n1>>n2;
cout<<“The sum is “<<sum(n1, n2);
}

Here the variable s is declared outside of all functions and we can use variable s anywhere in the program.

Kerala State Board New Syllabus Plus Two Computer Application Notes Chapter 2 Arrays.

Kerala Plus Two Computer Application Notes Chapter 2 Arrays

An array is a collection of elements with same data type Or with the same name we can store many elements, the first or second or third etc can be distinguished by using the index(subscript). The first element’s index is 0, the second element’s index is 1, and so on.

Declaring arrays
Suppose we want to find the sum of 100 numbers then we have to declare 100 variables to store the values. It is laborious work. Hence the need for an array arises.

Syntax: data_type array_name[size];

To store 100 numbers the array declaration is as follows
int n[100]; By this, we store 100 numbers. The index of the first element is 0 and the index of last element is 99.

Memory allocation for arrays
The amount of memory requirement is directly related to its type and size.
int n[100]; It requires 2 Bytes (for each integer)*100 = 200 Bytes.
float d[100]; It requires 4 Bytes(for each float)*100 = 400 Bytes.

Array initialization
Array can be initialized in the time of declaration.
Eg. int age[4] = {16, 17, 15, 18};

Accessing elements of arrays
Normally loops are used to store and access elements in an array.
Eg.

int mark[50], i;
for(i=0; i<50; i++)
{
cout<<“Enter value formark”<<i+1; cin>>mark[i];
}
cout<<“The marks are given below:’’;
for(i=0; i<50; i++)
cout<<mark[i];

Kerala State Board New Syllabus Plus Two Maths Previous Year Question Papers and Answers.

Kerala Plus Two Maths Previous Year Question Paper Say 2018 with Answers

Board	SCERT
Class	Plus Two
Subject	Maths
Category	Plus Two Previous Year Question Papers

Time : 2 1/2 Hours
Cool off time : 15 Minutes
Maximum : 80 Score

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 questions and to plan your answers.
• Read questions carefully before you answering.
• Read the instructions carefully.
• 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 to 7 carry 3 scores each. Answer any 7 questions.

Question 1.
a) Construct a 2 × 2 matrix whose elements are given a_ij = 2i + j
b) Find A².
Answer:

Question 2.
a) If \(\int \frac{f(x)}{x^{2}+1} d x\) = log | x² + 1 | + C, then f(x) = …………
b) Find ∫ xe^x dx
Answer:
a) f(x) = 2x
b) ∫ xe^x dx = x∫e^x dx – ∫1 × e^x dx
= xe^x – e^x + c = e^x (x – 1) + c

Question 3.
Form the differential equation of the family of all circles touching the y-axis at origin.
Answer:
Equation of the family of circle which touches the y-axis at origin is of the form.
(x – a)² + y² = a² ……… (1)

Question 4.
Consider the relation in the set N of Natural numbers defined as R = { (a,b): ab is a factor of 6}. Determine whether the relation is reflexive, symmetric or transitive.
Answer:
(2, 2) ∉ R, Not reflexive
(x, y) ∈ R ⇒ (y, x) ∈ R ⇒ xy = yx, Symmetric
(3, 2) ∈ R, (2, 3) ∈ R ⇒ (3, 3) ∉ R,
Since 3 × 3 = 9, not transitive.

Question 5.
Find the area bounded by the curve y= cos x and x axis between x = 0 and x = π.
Answer:
Area = 2 \(\int_{0}^{\pi / 2}\) cos xdx
= 2 \([\sin x]_{0}^{\pi / 2}\) = 2[1 + 0] = 2

Question 6.

A rectangular plot is to be fenced using a rope of length 20 meters with one of its sides is a wall as shown in the figure. Find the maximum area of such rectangle.

Length = 20 – 2x, breadth = x
A = x(20 – 2x) = 20x – 2x²
A'(x) = 20 – 4x ⇒ A'(x) = 0 ⇒ x = 5
A”(x) = -4 < 0
Hence A is maximum at x = 5
Maximum area = 5 × 10 = 50

Question 7.
A manufacture produces nuts and bolts. The time required to produce one packet of nuts and one packet of bolts on machines A and B is given in the following table

	Machine A	Machine B
Nuts (1 packet)	2 hours	3 hours
Bolts (1 packet)	3 hours	1 hour

He earns a profit of Rs. 25 per packet of nuts and Rs. 12 per packet of bolts. He operates his machines for almost 15 hours a day. Formulate a linear programming problem to maximise his profit.
Answer:
Maximise: Z = 25x + 12y
Subject to
2x + 3y ≤ l5; 3x + y ≤ 5; x, y ≥ 0

Questions 8 to 17 carry 4 scores each. Answer any 8.

Question 8.
Consider the curve y = x³ + 8x + 3
a) Find the point on the curve at which the slope of the tangent is 20.
b) Does there exist a tangent to the curve with negative slope? Justify your answer.
Answer:
a) \(\frac{d y}{d x}\) = 3x² + 8
Slope is given as 20
20 = 3x² + 8 ⇒ x = ±2
Therefore points (2, 27), (-2, -21)
b) No. 3x² + 8 ≥ 0 (Always positive for any value of x.)

Question 9.
a) Which of the following functions is not continuous at zero?
i) f(x) = sin x

b) Find the Values of a and b such that the function defined by
f(x) = \(\left\{\begin{array}{cc}
10, & x \leq 3 \\
a x+b, & 3<x<4 \\
20, & x \geq 4
\end{array}\right.\)
[Here f(x) is oscillating between -1 and 1 as x approaches to 0. In other cases the limit value and function value are same. So continuous.]
b) \(\lim _{x \rightarrow 3^{+}}\)f(x) = 3a + b ⇒ 3a + b = 10
\(\lim _{x \rightarrow 4^{-}}\) f(x) = 4a + b ⇒ 4a + b = 20
Solving both equations we get a = 10, b = -20

Question 10.
Consider the plane 2x – 3y + z = 5
a) Find the equation of the plane passing through the point (1, 1, 3) and parallel to the above plane.
b) Find the distance between above planes
Answer:
a) Equation of a plane parallel to the
2x – 3y + z = 5 is of the form 2x – 3y + z = k .
Since it passes through the point (1, 1, 3),
we have 2 – 3 + 3 = k ⇒ k = 2
⇒ 2x – 3y + z = 2

b) Distance between the planes
= \(\left|\frac{5-2}{\sqrt{4+9+1}}\right|=\frac{3}{\sqrt{14}}\)

Question 11.
Consider the vectors
\(\vec{a}\) = 2i + j + 3k; \(\vec{b}\) = i + 4j – k
a) Find the projection of \(\vec{a}\) on \(\vec{b}\)
b) If \(\vec{a}\) is perpendicular to a vector \(\vec{c}\) then projection of \(\vec{a}\) on \(\vec{c}\)
c) Write a vector \(\vec{d}\) such that the projection of \(\vec{a}\) on \(\vec{d}\) = |\(\vec{a}\)|
Answer:

b) Projection will be zero.
c) Projection of \(\vec{a}\) on \(\vec{d}\) = |\(\vec{a}\)|, means the angle between \(\vec{a}\) and \(\vec{d}\) is zero. Hence both are parallel. So any vector parallel to \(\vec{a}\) is \(\vec{d}\).

Question 12.
a)

In the figure ABCD is a Parallelogram. If
\(\overrightarrow{A B}\) = 3i – j + 2k; \(\overrightarrow{A D}\) = i + j + 2k, find \(\overrightarrow{A C}\) and \(\overrightarrow{D B}\)
b) If \(\vec{a}\) and \(\vec{b}\) are adjacent sides of any parallelogram \(\vec{c}\) and \(\vec{d}\) are diagonals,
then show that |\(\vec{c}\) × \(\vec{d}\)| = 2|\(\vec{a}\) × \(\vec{b}\)|
Answer:
a) \(\overrightarrow{A C}\) = \(\overrightarrow{A B}\) + \(\overrightarrow{A D}\) = 4i + 4j
\(\overrightarrow{B D}\) = \(\overrightarrow{A B}\) – \(\overrightarrow{A D}\) = 2i – 2j

b) Let \(\vec{c}\) = \(\vec{a}\) + \(\vec{b}\) and d = \(\vec{a}\) – \(\vec{b}\)
\(\vec{c}\) × \(\vec{d}\) = (\(\vec{a}\) + \(\vec{b}\)) × (\(\vec{a}\) – \(\vec{b}\))
= \(\vec{a}\) × \(\vec{a}\) – \(\vec{a}\) × \(\vec{b}\) + \(\vec{b}\) × \(\vec{a}\) – \(\vec{b}\) × \(\vec{b}\)
= 0 – \(\vec{a}\) × \(\vec{b}\) – \(\vec{a}\) × \(\vec{b}\) – 0 = -2(\(\vec{a}\) × \(\vec{b}\))

Question 13.
Find ∫(4x + 7)\(\sqrt{x^{2}+4 x+13}\)dx
Answer:
4x + 7 = A(2x + 4) + B ⇒ A = 2, B = -1
I = 2∫\(\sqrt{x^{2}+4 x+13}\)dx – ∫\(\sqrt{x^{2}+4 x+13}\)dx
I = 2I₁ – I₂

Question 14.
a) Write integrating factor of the linear differential equation \(\frac{d y}{d x}+\frac{y}{x}\) = sin x
b) Slope of the tangent to a curve at any point is twice the x coordinate of the point. If the curve passes through the point (1, 4), find its equation.
Answer:
IF = \(e^{\int P d x}\) = \(e^{\log x}\) = x
b) \(\frac{d y}{d x}\) = 2x ⇒ dy = 2x dx
Integrating we get;
∫dy = ∫ 2x dx + C ⇒ y = x² + C
Since passes through (1, 4) we have;
4 = 1 + C ⇒ C = 3
Hence equation is y = x² +3

Question 15.
Solve the linear programming problem graphically Maximise Z = 3x + 5y
Subject to the constraints
x + 3y ≤ 3
x + y ≤ 2
x, y ≥ 0

Corner points	Z = 3x + 5y
O (0, 0)	0
A (2, 0)	6
B\( \left(\frac{3}{2}, \frac{1}{2}\right)\)	7
C (0, 1)	5

Maximum 7 at B = \(\left(\frac{3}{2}, \frac{1}{2}\right)\)

Question 16.
a) If cos^-1 \(\frac{12}{13}\) = tan^-1 x then find x.
b) Show that cos^-1 \(\frac{4}{5}\) + cos^-1 \(\frac{12}{13}\) = tan^-1 \(\frac{14}{33}\)
Answer:

Question 17.
Consider the binary operation * on the set R of real numbers, defined by a*b = \(\frac{a b}{4}\)
a) Show that * is commutative and associative.
b) Find the identity element for * o R.
c) Find the inverse of 5.
Answer:

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

Question 18.
Consider the matrix A = \(\left[\begin{array}{lll}
1 & 0 & 2 \\
0 & 1 & 2 \\
0 & 4 & 9
\end{array}\right]\)
a) Find A^-1 using elementary row operations.
b) Find the solution of the system of equations given below:
(A^-1 obtained above may be used)
x + 2z + 2; y + 2z + 1; 4y + 9z = 3
Answer:
a) A = IA
\(\left[\begin{array}{lll}
1 & 0 & 2 \\
0 & 1 & 2 \\
0 & 4 & 9
\end{array}\right]=\left[\begin{array}{lll}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{array}\right] A\)

Question 19.
a) Show that
\(\left|\begin{array}{lll}
1 & a & b c \\
1 & b & a c \\
1 & c & a b
\end{array}\right|\) = (a – b)(b – c)(c – a)
b) If A = \(\left[\begin{array}{cc}
2 & 3 \\
4 & -1
\end{array}\right]\) verift that A × adj A = |A|I
Answer:

Question 20.
a) If f is a function such that f(-x) = f(x), then \(\int_{-a}^{a}\) f(x) dx = ………
b) Evaluate \(\int_{-\pi / 2}^{\pi / 2}\) cos x dx
c) Evaluate \(\int_{0}^{1}\) (x² + 1)dx as the limit of a sum.
Answer:

Question 21.
a) Verify mean value theorem for the function f(x) = x² – 4x – 3 in the interval [1, 4].
b) Consider the function
f(x) = sin^-1 2x \(\sqrt{1-x^{2}}\), \(\frac{-1}{\sqrt{2}} \leq x \leq \frac{1}{\sqrt{2}}\)
i) Show that f(x) = 2sin^-1 x
ii) Find f'(x)
Answer:
a) f(x) is a continuous function in [1, 4], since it is a polynomial.
f'(x) = 2x – 4, f is differentiable in (1, 4).
f(4) = 16 – 16 – 3 = -3, f(1) = 1 – 4 – 3 = -6

Hence mean value theorem is verified.

b) i) Put x = sinθ
f(x) = sin^-1 (2 sin θ\(\sqrt{1-\sin ^{2} \theta}\))
= sin^-1 (2 sin θ cos θ)
= sin^-1 (sin 2θ) = 2θ = 2 sin^-1 x
ii) f'(x) = \(\frac{2}{\sqrt{1-x^{2}}}\)

Question 22.
a) Show that the lines
\(\frac{x-2}{1}=\frac{y+1}{2}=\frac{z-3}{1} ; \frac{x-3}{2}=\frac{y-1}{1}=\frac{z-4}{2}\) are coplanar.
b) Find the equation of the plane that contains the above lines.
c) Show that the above lines intersect at the point (3, 1, 4).
Answer:
a) Points (2, -1, 3) and (3, 1, 4)

Normal direction ratios are 3, 0, -3.
Therefore equation of the plane is
3(x – 2) -3 (z – 3) = 0
3x – 6 – 3z + 9 = 0
x – z + 1 = 0

c) (3, 1, 4) is a point on the second line. Substitute the point in the first line
\(\frac{3-2}{1}=\frac{1+1}{2}=\frac{4-3}{1} \Rightarrow \frac{1}{1}=\frac{2}{2}=\frac{1}{1}\)
Therefore the point (3, 1, 4) satisfies the first line. Hence both interest at (3, 1, 4).

Question 23.
a) A coin is tossed 3 times. Find the probability distribution of the number of heads.
b) A bag contains 5 black and 6 white balls, 4 balls of the same colour (Black or white) are added to the bag, shuffled well and one ball is drawn. If the ball obtained is white. What is the probability that the balls added are black?
Answer:
a) Let X be the random variable denoting the
number of heads appears. Then X = {0, 1, 2, 3}
P(X = x) = ⁿC_x P^xq^n-x; p = \(\frac{1}{2}\), q = \(\frac{1}{2}\), n = 3

X	0	1	2	3
P(X)	\(\frac{1}{8}\)	\(\frac{3}{8}\)	\(\frac{3}{8}\)	\(\frac{1}{8}\)

E₁ = Balls added are black.
E₂ = Balls added are white.
A = Ball drawn is white.

Question 24.

In a circle of radius 2 a square is inscribed as shown in the figure. Using integration, find the area of the shaded region (Area of a square may be calculated using any convenient method)
Answer:

Equation of the circle is x² + y² = 4
Area of the sector in the first quadrant

Area of the triangle = \(\frac{1}{2}\) (2)(2) = 2
Area of the shaded region in the first quadrant = π – 2
Hence the area of the required region = 4(π – 2) = 4π – 8

Kerala State Board New Syllabus Plus Two Computer Application Notes Chapter 1 Review of C++ Programming.

Kerala Plus Two Computer Application Notes Chapter 1 Review of C++ Programming

It is developed by Bjame Stroustrup. It is an extension of C Language.

Character set: To study a language first we have to familiarize the character set. For example to study English language first we have to study the alphabets. Similarly here the character set includes letters (A to Z & a to z), digits (0 to 9), special characters(+, -, ?, *, /, …….) white spaces(non printable) etc….

Token: It is the smallest individual units similarto a word in English or Malayalam language. C++ has 5 tokens
1. Keywords: These are reserved words for the compiler. We can’t use for any other purposes.
Eg: float is used to declare variable to store numbers with decimal point. We can’t use this for any other purpose

2. Identifier: These are user defined words.
Eg: variable name, function name, class name, object name etc…

3. Literals (Constants): Its value does not change during execution
i. Integer literals : Whole numbers without fractional parts are known as integer literals, its value does not change during execution. There are 3 types decimal, octal and hexadecimal.
Eg. For decimal 100, 150, etc
For octal 0100, 0240, etc
For hexadecimal 0x100, 0x1A, etc

ii. Float literals: A number with fractional parts and its value does not change during execution is called floating point literals.
Eg. 3.14157, 79.78, etc..

iii. Character literal: A valid C++ character enclosed in single quotes, its value does not change during execution.
Eg. ‘m’, ‘f’, etc…

iv. String literal: One or more characters enclosed in double quotes is called string constant. A string is automatically appended by a null character (‘\0’)
Eg. “Mary’s”, “India”, etc

4. Punctuators: In English or Malayalam language punctuation marks are used to increase the readability but here it is used to separate the tokens. Eg: {,}, (,),

5. Operators: These are symbols used to perform an operation (Arithmetic, relational, logical, etc…)

Integrated Development Environment(IDE): It is used for developing programs

• It helps to write as well as editing the program.
• It helps to compile the program and linking it to other (header files and another user) programs
• It helps to run the program

Turbo C++ IDE
Following is a C++ IDE

a) Opening the edit window
Method I: File → Click the menu item
New Method II: Press Alt and F simultaneously then press N
b) Saving the program:
Click File → Save or Press Function key F2 or Alt + F and then press S
Then give a file name and press ok.
c) Running/executing the program
Press Alt + R then press R OR Click Run → press R, OR Press Ctrl + F9
d) Viewing the output: Press Alt + F5
e) Closing Turbo C++ IDE
Click File → then press Quit menu Or Press Alt + X

Geany IDE

Step 1: Take Geany Editor and type the program(source code)
Step 2: Save the file with the extension.cpp
Step 3: Compile the program by Click the Compile Option
Step 4: After successful compilation, Click the Build option
Step 5: Then click on the Execute option

Important Notes while using Geany Editor

1. For the header files .h extension need not given
2. Header files are given below

3. Add a new statement using namespace std; after the preprocessor
4. Instead of void main() use int main();

Let us see the following to distinguish the editor’s Turbo C++ and Geany

1. Write a C++ program to read a number and print.

Using Turbo C++ editor

#include
#include
int main()
{
clrscr();
int a;
cout<<“Enter a number”; cin>>a;
cout<<“The number you entered is ”<<a;
getch();
}

To compile and press Ctrl+F9.

Using Geany editor

#include
using namespace std;
int main()
{
int a;
cout<<“Enter a number”; cin>>a;
cout<<“The number you entered is ”<<a;
}

Type the above and save it as a file name with .cpp.
Compile, Build and then Execute

Concepts of data types: The nature of data is different, data type specifies the nature of data we have to store.

C++ data types

Fundamental data types: It is also called a built-in data type. They are int, char, float, double and void
i) int data type: It is used to store whole numbers without fractional (decimal point) part. It can be either negative or positive. It consumes 2 bytes(16 bits) of memory.i.e. 216 = 65536 numbers. That is 32768 negative numbers and 32768 positive numbers(0 is considered as +ve ) So a total of 65536 (32768+32768) numbers. We can store a number in between -32768 to + 32767.

ii) char data type: Any symbol from the key ‘ board, eg. ‘A’, ‘?’, ‘9’,…. It consumes one byte (8 bits) of memory. It is internally treated as integers, i.e. 28 = 256 characters. Each character is having an ASCII code, ‘a’ is having ASCI I code 97, and zero is having ASCII code 48.

iii) float data type: It is used to store real numbers i.e. the numbers with a decimal points. It uses 4 bytes(32 bits) of memory.
Eg. 67.89, 89.9 E-15.

iv) double data type: It is used to store very large real numbers. It uses 8 bytes(64 bits) of memory.

(v) void data type: void means nothing. It is used to represent a function that returns nothing.

User-defined Data types: C++ allows programmers to define their own data type. They are Structure(struct), enumeration(enum), union, class, etc.

Derived data types: The data types derived from fundamental data types are called Derived data types. They are Arrays, pointers, functions, etc

Variables:
The named memory locations are called variables. A variable has three important things

1. variable name: A variable should have a name
2. Memory address: Each and every byte of memory has an address. It is also called the location (L) value.
3. Content: The value stored in a variable is called content. It is also called Read(R) value.

Operators: An operator is a symbol that performs an operation. The data on which operations are carried out are called operands. Following are the operators
1) Input (>>) and output (<<) operators are used to performing input and output operations. Eg. cin >> n;
cout << n;

2) Arithmetic operators: It is a binary operator. It is used to perform addition(+), subtraction(-), division (/), multiplication(*) and modulus(%-gives the remainder) operations.
Eg. If x = 10 and y = 3 then

x/y = 3, because both operands are integer. To get the floating-point result one of the operands must be float.

3) Relational operator: It is also a binary operator. It is used to perform comparison or relational operation between two values and it gives either true (1) or false(0). The operators are <, <=, >, >=, == (equality) and != (not equal to)

4) Logical operators: Here AND(&&), OR(||) are binary operators, and NOT(!) is a unary operator.
It is used to combine relational operations and it gives either true (1) or false (0).
If x = 1 and y = 0 then

Both operands must be true to get a true value in the case of AND (&&) operation.
If x = 1 and y = 0 then

Either one of the operands must be true to get a true value in the case of OR(||) operation
If x = 1 and y = 0 then

5) Conditional operator: It is a ternary operator hence it needs three operands. The operator is ?:.
Syntax: expression ? value if true : value if false.
First evaluates the expression if it is true the second part will be executed otherwise the third part will be executed.
Eg. If x = 10 and y = 3 then
x > y ? cout<<x; cout<<y
Here the output is 10

6) sizeof(): This operator is used to find the size used by each data type.
Eg. sizeof(int) gives 2.

7) Increment and decrement operator: These are unary operators.
a) Increment operator (++): It is used to increment the value of a variable by one i.e., x++ is equivalent to x = x + 1;
b) Decrement operator (–): It is used to decrement the value of a variable by one i.e., x– is equivalent to x = x – 1.

8) Assignment operator (=): It is used to assign the value of the right side to the left side variable.
eg. x = 5; Here the value 5 is assigned to the variable x.

Expressions: It is composed of operators and operands

Arithmetic expression: It is composed of arithmetic operators and operands. In this expression the operands are integers then it is called the Integer expression. If the operands are real numbers then it is called Floating point expression. If the operands are constants then it is called constant expression.

Relational expression: It is composed of relational operators and operands.

Logical expression: It is composed of logical operators and operands

Statements: Statements are the smallest executable unit of a programming language. Each and every statement must end with a semicolon(;).

Declaration statement: Each and every variable must be declared before using it.
Eg: int age;

Assignment statements: The assignment operator is used to assign the value of RHS to LHS.
Eg: x = 100;

Input statements:
input(>>) operator is used to perform input operation. Eg. cin>>n;

Output statements
output(<<) operator is used to perform output operation.
Eg. cout<<n;

Cascading of I/O operations
The multiple uses of input or output operators in a single statement is called Cascading of i/o operators.
Eg: To take three numbers by using one statement is as follows
cin>>x>>y>>z;
To print three numbers by using one statement is as follows
cout<<x<<y<<z;

Structure of a C++ program:
A typical C++ program would contain four sections as shown below.
Include files(Preprocessor directives)
Function declarations
Function definitions
Main function programs
Eg:

# include
using namespace std;
int sum(int x, int y)
{return (x+y);}
intmain()
{
cout<<sum(2, 3);
}

Preprocessor directives: A C++ program starts with the preprocessor directive i.e., # include, #define, #undef, etc, are such a preprocessor directive. By using #include we can link the header files that are needed to use the functions. By using #define we can define some constants.
Eg. #define x 100. Here the value of x becomes 100 and cannot be changed in the program.
No semicolon is needed.

Header files:
header files: A header file is a pre-stored file that helps to use some operators and functions. To write C++ programs the header files are a must. Following are the header files used in Geany editor.
iostream
cstdio
cctype
cmath
cstring
cstdlib
The syntax for including a header file is as follows
#include<name of the header file>
Eg. #include<iostream>

The main function: The main function is the first function which is invoked at the time of execution and the program ends within main(). The other functions are invoked from main().

Programming tips:
The identifier name must be clear, precise, brief, and meaningful
Use clear and simple expressions.
Use comments wherever needed.
To give tips in between the program comments are used. A comment is not considered as the part of the program and cannot be executed. There are 2 types of comments single line and multiline. Single line comment starts with //(2 slashes) but multi-line comment starts with /* and ends with */
indentation: Giving leading spaces to the statements is called indentation. It is a good programming practice.

Variable initialisation: Giving value to a variable at the time of declaration.
Eg: intage=16; Here the OS allocates 4 bytes memory for the variable age and it stores a value 16.

const-The access modifier: By using the keyword const we can create symbolic constants its value does not change during execution.
Eg: const int bp=100;

Type modifiers: With the help of type modifiers we can change the sign and range of data with same size. The important modifiers are signed, unsigned, long and short

Shorthands in C++

Arithmetic assignment operators: It is faster. This is used with all the arithmetic operators as follows.

a) Increment operator(++): It is used for incrementing the content by one.
++x(pre increment) and x++ (post increment) both are equivalent to x = x + 1.

b) decrement operator (–): It is used for decrementing the content by one.
–x (pre decrement) and x– (post decrement) both are equivalent to x = x – 1.

Prefix form: In this, the operator is placed before the operand and the operation is performed first then use the value.

Postfix form: In this, the operator is placed after the operand and the value of the variable is used first then the operation is performed
Eg: Post increment a++
Here first use the value of ‘a’ and then change the value of ‘a’.
Eg: if a=10 then b=a++.
After this statement b=10 and a=11

Pre increment ++a
Here first change the value of a and then use the value of a.
Eg: if a=10 then b=++a.
After this statement b=11 and a=11.

Precedence of operators: Consider a situation where an expression contains all the operators then the operation will be carried in the following order(priority)

Type conversion: Type conversions are of two types.
1) Implicit type conversion: This is performed by the C++ compiler internally. C++ converts all the lower sized data type to the highest sized operand. It is known as type promotion. Data types are arranged lower size to higher size is as follows, unsigned int(2 bytes), int(4 bytes), long (4 bytes), unsigned long (4 bytes), float(4 bytes), double(8 bytes), long double(10 bytes)

2) Explicit type conversion: It is known as typecasting. This is done by the programmer. The syntax is given below.
(data type to be converted) expression
Eg. int x=10;
(float) x;
This expression converts the data type of the variable from integer to float.
These are classified into two decision making and iteration statements

Decision-making statements:

if statement:

Syntax: if (condition)
{
Statement block;
}

First, the condition is evaluated if it is true the statement block will be executed otherwise nothing will be happened.

if… else statement:

Syntax:

if (condition)
{
Statement block1;
}
Else
{
Statement block2;
}

Nested if
An if statement contains another if statement completely then it is called nested if.

if (condition 1)
{
if (condition 2)
{
Statement block;
}
}

The statement block will be executed only if both the conditions evaluated are true.

The else if ladder: The syntax will be given below:

if (expression 1)
{
statement block1;
}
else if (expression 2)
{
statement block 2;
}
else if (expression 3)
{
statement block 3;
}
..............
else
{
statement block n;
}

Here firstly, expression 1 will be evaluated if it is true only the statement block1 will be executed otherwise expression 2 will be evaluated if it is true only the statement block2 will be executed and so on. If all the expression evaluated is false then only statement block n will be executed.

switch statement:
It is a multiple branch statement. Its syntax is given below.

switch(expression)
{
case value: statements;break;
case value: statements;break;
case value: statements;break;
case value: statements;break;
case value: statements;break;
...............................
default: statements;
}

The first expression evaluated and selects the statements with the matched case value. If all values are not matched the default statement will be executed.

Conditional operator: It is a ternary operator hence it needs three operands. The operator is ?:.
Syntax: expression ? value if true : value if false.
First evaluates the expression if it is true the second part will be executed otherwise the third part will be executed.

Iteration statements: If we have to execute a block of statements more than once then iteration statements are used.

while statement: It is an entry controlled loop. An entry controlled loop first checks the condition and executes (or enters into) the body of the loop only if it is true. The syntax is given below:

Loop variable initialised
while(expression)
{
Body of the loop;
Update loop variable;
}

Here the loop variable must be initialised before the while loop. Then the expression is evaluated if it is true then only the body of the loop will be executed and the loop variable must be updated inside the body. The body of the loop will be executed until the expression becomes false.

for statement
The syntax of for loop is

for(initialization; checking; update loop variable)
{
Body of loop;
}

The first part, initialization is executed once, then checking is carried out if it is true the body of the for loop is executed. Then the loop variable is updated and again checking is carried out this process continues until the checking becomes false. It is an entry controlled loop.

do-while statement: It is an exit controlled loop. Exit control loop first executes the body of the loop once even if the condition is false then checks the condition.

do
{
Statements
}while(expression);

Here the body executes at least once even if the condition is false. After executing the body it checks the expression if it false it quits the body otherwise the process will continue.