MA Economics Entrance Mock Tests

In how many ways can 11 players be chosen out of 15 if a particular player is never chosen :

In how many ways can 11 players be chosen out of 15 if a particular player is always chosen :

A committee of 5 is to selected from among 6 boys and 5 girls. Determine the number of ways of selection if the committee is to consist of at least one boy and one girl?

A cricket team of 11 players is to be selected from 16 players including 5 bowlers and 2 wicket keepers. In how many ways can a team be selected so as to consist of exactly 3 bowlers and one wicket keeper?

A box contains two white balls, three black balls, and four red balls. In how many ways can three balls be drawn from the box if at least one black ball is to be included in the draw?

A candidate is required to answer 7 questions out of 12 questions which are divided into two groups of 6 questions each. He is not permitted to attempt more than 5 questions from either group. In how many ways can he choose 7 questions?

From a class of 25 students, 10 are to be chosen for an excursion. There are 3 students who decide that either all of them will join or none of them will join. In how many ways can they be chosen ?

A certain club consists of 5 men and 5 women. A 5-member committee consisting of 2 men and 3 women has to be constituted. Also, suppose that Mrs. F refuses to work with Mr. M.

How many ways are there of constituting a 5-member committee that ensures that both of them do not work together?

A certain club consists of 5 men and 5 women. A 5 member committee consisting of 2 men and 3 women has to be constituted. How many ways are there of constituting this committee?

A committee consisting of 3 men and 2 women is to be formed out of 6 men and 4 women. In how many ways this can be done if Mr. X and Mrs. Y are not to be included together?

Two patients share a hospital room for two days. Suppose that, on any given day, a person independently picks up an airborne infection with probability 1/4. An individual who is infected on the first day will certainly pass it to the other patient on the second day. Once contracted, the infection stays for at least two days. What is the probability that fewer than two patients have the infection by the end of the second day? 

Suppose 1/10 of the population has a disease. If a person has the disease, then a test detects it with probability 8/10. If a person does not have the disease, then the test incorrectly shows the presence of the disease with probability 2/10. What is the probability that the person tested has the disease if the test indicates the presence of the disease?

There are 3 red and 5 black balls in an urn. You draw two balls in succession without replacing the first ball.
The probability that the second ball is red equals

An insurance policy-holder can submit up to 5 claims. The probability that the policyholder submits exactly n claims is p_n, for n = 0, 1, 2, 3, 4, 5. It is known that
(a)  The difference between p_n and p_{n + 1} is constant for n = 0, 1, 2, 3, 4, and 

(b)  40% of the policyholders submit 0 or 1 claim.
What is the probability that a policy-holder submits 4 or 5 claims?

A tour operator has a bus that can accommodate 20 tourists. The operator knows that tourists may not show up, so he sells 21 tickets. The probability that an individual tourist will not show up is 0.02, independent of all other tourists. Each ticket costs 50, and is non-refundable if a tourist fails to show up. If a tourist shows up and a seat is not available, the tour operator has to pay 100 to that tourist. The expected revenue of the tour operator is 

In a roll of two fair dice, X is the number on first die and Y is the number on second die. Which of the following statements is True

A family has two children, what is the probability that both are girls given that at least one child is girl?

A student is answering a multiple‐choice examination. Suppose a question has m possible answers. The student knows the correct answer with probability p. If the student knows the correct answer, then she picks that answer; otherwise, she picks randomly from the choices with probability 1/m each. Given that the student picked the correct answer, the probability that she knew the correct  answer is

Suppose two fair dice are tossed simultaneously. What is the probability that the total number of spots on the upper faces of the two dice is not divisible by 2, 3, or 5?

A coin toss has possible outcomes H and T with probabilities 3/4 and 1/4 respectively. A gambler observes a sequence of tosses of this coin until H occurs. Let the first H occur on the n^th toss. If n is odd, then the gambler’s prize is −2ⁿ , and if n is even, then the gambler’s prize is 2ⁿ . What is the expected value of the gambler’s prize?

Which of the following is not a monotonic transformation

An Indirect Utility function

Suppose a consumers preferences over commodities 1 and 2 can be represented by utility function U(x1, x2) = min{x1, x2} where x1, x2 ≥ 0. The utility function of the consumer is

Which of the following represents the same preferences as U(x1, x2) = min{x1, x2} + max{x1, x2}

Which of the following represents the same preferences as U(x1, x2) = min{x1, x2} + max{x1, x2}

For a utility function representing strictly convex preferences, the marginal rate of substitution between two commodities must be

Suppose a consumer’s preference are given by the utility function u =4(x^0.5) + y . Suppose the consumer’s original equilibrium was x = 9, y = 10. If the consumption of x reduces to 4, how many units of y must he consume to remain on the same indifference curve?

Rohit consumes soft drink which is available in ½ litre and 1 litre bottles. He allows himself only half litre of soft drink at a time, so if he has a bottle of 1 litre he will throw ½ litre in the sink. Considering 1/2 litre bottle as good 1, what is his utility function

A consumer is indifferent between two hamburgers (good 1) and 3 Puri's (good 2) so his indifference curves are

A consumer is indifferent between two hamburgers (good 1) and 3 Puri's (good 2) so his utility function is 

Investment increases proportionately with the increase in capital stock implies that, for a given rate of saving _______

In the Solow Model, The production function becomes __________ as k increases indicating that it gives _____________ marginal product of capital

The aggregate production function for the Solow growth model assumes (A) ___________ returns to scale and (B) _____________marginal productivity of labour and capital.

In the Solow Model, the point where investment is equal to depreciation is known as the ______________.

According to the Solow Model, _____________________ is a function of capital.

Consider an economy described by the following production function :

F(K, L) = K^0.5L^0.5  

Assume that the rate of depreciation is 10% per year and rate of saving is 30%. Find the steady state level of Investment of Solow’s model.

Consider an economy described by the following production function :

F(K, L) = K^0.5L^0.5  

Assume that the rate of depreciation is 10% per year and rate of saving is 30%. Find the steady state capital stock per worker of Solow’s model.

In the Solow Model, the change in saving rate produces

In the Solow Model, the economy which is not at steady state

In the Solow Model, at the steady state we have