# Category: Mathematics

## Integration by Partial Fraction

Practice Questions 1. Ans : 2. Ans : 3. Ans : 4. Ans : 5. Ans : 6. Ans : 7. Ans : 8. Ans : 9. Ans : 10. Ans : 11. Ans : 12. Ans : 13. Ans : 14. Ans. 15. Ans :

## Applications of Differentiation in Economics [Maxima & Minima]

Applications of Differentiation in Economics 1. The total cost C (x) associated with producing and marketing x units of an item is given by , Find a) Total cost when output is 4 units. b) Average cost of output of 10 units. c) Marginal cost when output is 3 units. 2. Find (i) the average total cost …

## Cobweb Model as an Application of Difference Equation

Let the demand and supply function as and According to the above equations the demand of the commodity depends on the current price of the commodity and the supply depends on the prices of previous period denoted by  respectively. As we know at equilibrium, or or  ——————- (A) This (A) is the basic equation of the …

## The Slutsky Equation

Decomposition of Price Effect into Income and Substitution Effect Change in the price and income alters the consumer’s expenditure pattern. So to know the consumer’s expenditure pattern due to change in price and income all the variables should be varied simultaneously. Let, Utility function be Subject to Or Here we can form a new function with …

## Compensated Demand Function

Suppose there is a situation in which government imposes taxes or subsidies a consumer in such a way so as to leave his utility unchanged after a price change. Lets assume this is done by lump sum payment that will give the consumer the minimum income necessary to achieve his initial utility level. The compensated demand …

## Ordinary Demand Function

A consumer’s ordinary demand function sometimes also called a Marshallian demand function gives the quantity of a commodity that he will buy as a function of commodity prices and his income. They can be derived from the analysis of utility maximisation. Let the utility function is  and the budget constraint as . Form the expression  And set …

## Maximization of Utility

The maximisation of utility The rational consumer desire to purchase a combination of x1 and x2 form which he derives the highest level of satisfaction. His problem is one of maximisation. However, his income is limited, and he is not able to purchase unlimited amount of the commodities. The consumer’s budget constraint can be written as  …

## Questions on Counting Techniques and Probability

Questions on Counting Techniques and  Probability  1. How many 4 even numbers can be formed by using 7,4,6,9 ? 2. How many 4 digit numbers can be formed by using 5,7,9,0? 3. How many 4 digit numbers can be formed by using 5,7,9,0 when the digits can be repeated ? 4. How many words with or …

## Linear Programming [Word Problems]

Linear Programming Practice Questions A manufacturer produces two types of steel trunks. He has two machines A and B. The first type of trunk requires 3 hours on machine A and 3 hours on machine B. The second type requires 3 hours on machine A and 2 hours on machine B. Machine A and B work …

## F – Test

F-Test F- test is generally known as the arcane ratio test and it is used mostly in  context of analysis of variance. This technique was developed by Prof.Fisher. Prof. Fisher developed this test on the basis of agricultural experiment. For test of hypothesis of equality among several sample means. The F-test is considered to be more …