List of top Questions asked in Indian Institute Of Technology Joint Admission Test for MSc- 2024

In the case of a small open economy with fixed exchange rate regime and imperfect capital mobility, which of the following is/are CORRECT?

Let $X_1, X_2, … , X_𝑛$ be a random sample of size n > 1 drawn from a probability distribution having mean $\mu$ and non-zero variance $\sigma^2$. Then, which of the following is/are CORRECT?

Let a random variable X has mean $\mu_x$ and non-zero variance $ \sigma ^2 _x$, and another X random variable Y has mean $\mu_y$ and non zero variance $\sigma ^2 _y$. If the correlation Y coefficient between X and Y is $\rho$, then which of the following is/are CORRECT?

Consider two independent random variables: $X ∼ N(5, 4)$ and $Y~N(3, 2)$. If $(2X + 3Y)~N(\mu, \sigma ^2)$, then the values of mean ($\mu$) and variance ($\sigma ^2$) are

Two distinct integers are chosen randomly from 5 consecutive integers. If the random variable x represents the absolute difference between them, then the mean and variance of x are, respectively,

Suppose a random variable 𝑋 follows an exponential distribution with mean 50. Then, the value of the conditional probability $ P(X > 70 | X > 60)$ is

Let 𝑥 and 𝑦 be two consumption bundles, assumed to be non-negative and perfectly divisible. Further, the assumptions of completeness, transitivity, reflexivity, non-satiation, continuity, and strict convexity are satisfied. Then, which of the following statements is NOT CORRECT?

Which one of the following is a non-parametric test?

There are 32 students in a class. Three courses namely English, Hindi and Mathematics are offered to them. Each student must register for at least one course. If 16 students take English, 8 students take Hindi, 18 students take Mathematics, 4 students take both English and Hindi, 5 students take both Hindi and Mathematics, and 5 students take both English and Mathematics, then the number of students who take Mathematics only is (in integer).

Two students 𝐴 and 𝐵 are assigned to solve a problem separately. The (conditional) probability that 𝐴 can solve the problem given that 𝐵 cannot solve it, is 1/5. The (conditional) probability that 𝐵 can solve the problem given that 𝐴 can solve the problem is 3/5 . The probability that 𝐴 can solve the problem is 1/10/
Then, the probability that 𝐵 can solve the problem is ______ (rounded off to one decimal place).

Let the value of a random sample drawn from a normal distribution with mean 5 and unknown standard deviation $\sigma$ be 4.8, 4.5, 5.1, 5.2, 5.3, 5.5. Then, the maximum likelihood estimate of $\sigma^2$ is _____. (rounded off to two decimal places).

A regression equation 𝑌 = −2.5 + 2𝑋 is estimated using the following data:

𝑌	2	5	9	14
𝑋	2	4	6	8

The coefficient of determination is ________ (rounded off to two decimal places).

The characteristics of pure public good is/are

Consider the following three utility functions:
$F = (4x_1 + 2x_2), G = min (4x_1, 2x_2)$ and $H = (\sqrt{x_1} + x_2)$ where, $x_1$ and $x_2$ are two goods available at unit prices $p_{x1}$ and $p_{x2}$ , respectively. Which of the following is/are CORRECT for the above utility functions?

Suppose high quality and low quality products are sold at the same price to the buyers. The buyers have less information to determine the quality of the product compared to the sellers at the time of purchase. Which of the following problems arises in this situation?

Consider a closed economy with consumption function $ C = 2 + 0.5𝑌$, where 𝑌 is income. The government expenditure is 3 and investment function is $ I = 4 − 0.5r $ , where r is interest rate. Then, the slope of the IS curve will be

Consider a production function of the form:
$ Y = 𝑎 log L + (1 − 𝑎) log K , 𝑎 ∈ (0, 1), 𝑎 ≠ 0.5 $
where, Y is output, L is labour, and K is capital. Then, the absolute value of elasticity of substitution is

Let an inverse demand function for a commodity be $𝑝 = e^{\frac{-x}{2}$, where 𝑥 is the quantity and 𝑝 is the price. Then, at 𝑝 = 0.5, the consumer surplus is equal to _______ (rounded off to two decimal places).

There are two goods 𝑋 and 𝑌 and there are two consumers 𝐴 and 𝐵 in a pure exchange economy. 𝐴 and 𝐵 have Cobb-Douglas utility functions of the form $𝑈_𝐴 = 2𝑋^{0.4} 𝑌^{0.6}$ and $𝑈_𝐵 = 𝑋^{0.3}𝑌^{0.7}$, respectively. Initially, 𝐴 is endowed with 50 units of good 𝑋 and 20 units of good 𝑌. Similarly, 𝐵 is endowed with 50 units of good 𝑋 and 20 units of good 𝑌. If the unit price of good 𝑌 is normalised to 1, then the equilibrium unit price for good 𝑋 is _____. (rounded off to two decimal places).

An industry has 6 firms in Cournot competition. Each of the 6 firms has zero fixed costs, and a constant marginal cost equal to 20. The product is homogenous and the industry inverse demand function is given by 𝑃 = 230 − 𝑄, where 𝑃 is the market price and 𝑄 is the industry output (sum of outputs of the 6 firms). The market price under Cournot-Nash equilibrium is equal to _____ (in integer).

A consumer’s utility function is given by: $𝑢(𝑥_1, 𝑥_2) = (2𝑥_1 − 1)0.25(𝑥_2 − 4)0.75$ If the consumer has a budget of 73 and the unit prices of $𝑥_1$ and $𝑥_2$ are given by 2 and 1, respectively, then the value of ($𝑥_1 + 𝑥_2$) is ________ (rounded off to two decimal places).

Let $f ∶ R^2 → R$ be a function defined as
$f(x,y) =\begin{cases}\frac{x^2y}{x^4 + Y^2} & if (x, y) \neq (0, 0)\\ 0 & if (x, y) = (0, 0)\end{cases} $ Then, which of the following is/are CORRECT?

Let $M =\begin{bmatrix} \alpha & − 6 \\-1 & -1 \end{bmatrix}, \alpha\, \epsilon\, R $ be a 2 × 2 matrix. If the eigenvalues of $M$ are $\beta$ and 4, then which of the following is/are CORRECT?

The differential equation satisfied by circles with radius 3 and center lying on the Y-axis is

In a two-player game, player 1 can choose either U or D as strategies. Player 2 can choose either L or R as strategies. Let 𝑐 be a real number such that $0 < 𝑐 < 1$. If the payoff matrix is

	L	R
U	0, 0	0, −c
D	−c, 0	1 − c, 1 − c

then the number of pure strategy Nash Equilibria in the game equals