List of top Questions asked in IIT JAM EN

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,

Let $S_1 = {(x, y) ∈ R^2 ∶ x + y ≥ 1, x + y ≤ 2, y ≥ x^2, x, y ≥ 0}$ and $S_2 = {(x, y) ∈ R^2 ∶ x + y ≥ 1, x + y ≤ 2, y ≤ x^2, x, y ≥ 0}.$ Then, which of the following is CORRECT ?

Suppose nominal GDP equals 1,000 units and money supply equals 250 units. Based on the quantity theory of money, the velocity of money equals

Which of the following measures was NOT initiated by the Government of India as a part of economic reforms in 1991?

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

Which of the following was announced in the Union Budget 2023-24 to enhance the skills of lakhs of youth in the next 3 years?

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 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?

Using the following table,

Year	Population of the Economy	GDP of the Economy (in crore)
2010	20,000	25,000
2020	25,000	40,000

the average growth rate (compounded annually) of per capita GDP in an economy during the period 2010-2020 is ________ (in percent, round off to 2 decimal places).

GDP_F = Gross Domestic Product at Factor Cost; GDP_M = Gross Domestic Product at Market Price; NNP_F= Net National Product at Factor Cost; C = Consumption; I = Investment; G = Government Expenditure; X = Export; M = Import; T = Tax; S = Saving; D = Depreciation; NIA = Net Income from Abroad
Which of the following expressions is/are CORRECT?

Consider a Keynesian Cross Model with following features,
Consumption Function: C = C0 + b(Y-T) 
Tax Function: T = T0 + tY 
Income Identity: Y = C + I0 + G0 
Where, C = Consumption; Y = Real Income; T = Tax; I = Investment; 
G = Government Expenditure; b = Parameter; t = Tax Rate 
(The subscript 0 (zero) indicates that the concerned variable is autonomous) 
If b = 0.7 and t = 0.2, value of the Keynesian multiplier is ________ (round off to 2 decimal places).

Let ∫ sin⁹ 𝑥 cos(11𝑥) 𝑑𝑥 = cos(10𝑥) 𝑓(𝑥) + 𝑐 , where 𝑐 is a constant. If 𝑓 ′′ (\(\frac{\pi}{4}\)) − 𝑘𝑓 ′(\(\frac{ \pi}{4}\)) = 0, then 𝑘 is equal to ______ (in integer)

Let [𝑡] denote the greatest integer ≤ 𝑡. The number of points of discontinuity of the function 𝑓(𝑥)= [𝑥²−3𝑥+2] for 𝑥∈[0, 4] is _______ (in integer)

Let 𝑀 = \(\begin{bmatrix} K & 1 & 1 \\ 1 & K & 1 \\ 1 & 1 & K \end{bmatrix}\)and I₃ be the identity matrix of order 3. If the rank of the matrix 10 𝐼₃ − 𝑀 is 2 then 𝑘 is equal to _____ (in integer).

Let 2𝑧=-3+√3 𝑖 , 𝑖 = √−1. Then 2z ⁸ is equal to

Let the probability density function of the continuous random variable 𝑋 be
, 0, 𝑥 ≥ 0 otherwise , 
where 𝜆 > 0 is a parameter. If the observed sample values of 𝑋 are 
𝑥₁ = 1.75, 𝑥₂ = 2.25, 𝑥₃ = 2.50, 𝑥4 = 2.75, 𝑥₅ = 3.25, then the Maximum Likelihood Estimator of 𝜆 is

Two people, 1 and 2, are engaged in a joint project. Person 𝑖∈{1,2} puts in effort 𝑥𝑖 (0≤ 𝑥𝑖 ≤ 1), and incurs cost 𝐶_𝑖 (𝑥_𝑖 ) = 𝑥_𝑖 . The monetary outcome of the project is 4𝑥₁𝑥₂ which is split equally between them. Considering the situation as a strategic game, the set of all Nash Equilibria in pure strategies is

Let 𝑋 ∼ 𝑈𝑛𝑖𝑓𝑜𝑟𝑚 8, 20) and 𝑍 ∼ 𝑈𝑛𝑖𝑓𝑜𝑟𝑚(0, 6) be independent random variables. Let 𝑌 = 𝑋 + 𝑍 and 𝑊 = 𝑋 − 𝑍. Then 𝐶𝑜𝑣(𝑌, 𝑊) is ______ (in integer).

An economy has three firms: X, Y and Z. Every unit of output that X produces creates a benefit of INR 700 for Y and a cost of INR 300 for Z. Firm X’s cost curve is
\(𝐶(𝑄_𝑋) = 2𝑄^2_X + 10\)
where 𝐶 represents cost and 𝑄_𝑋 is the output. The market price for the output of X is INR 1600 per unit. The difference between the socially optimal output and private profit maximizing output of firm X (in INR) is _____ (in integer).

Consider an Economy that produces only Apples and Bananas. The following Table contains per unit price (in INR) and quantity (in kg) of these goods. Assuming 2010 as the Base Year and using GDP deflator to calculate the annual inflation rate, which of the following options is CORRECT?

Year	Price of Apple	Quantity of Apple	Price of Banana	Quantity of Banana
2010	1	100	2	50
2011	1	200	2	100
2012	2	200	4	100

Let the joint probability density function of the random variables 𝑋 and 𝑌 be
\(f(x,y) =   \begin{cases} 1,     & \quad 0<x<1,\,\,\,\,x<y<x+1\\   0,& \quad \ \text{ Otherwise}   \end{cases}\)
Let the marginal density of 𝑋 and 𝑌 be 𝑓_𝑋(𝑥) and 𝑓_𝑌 (𝑦), respectively. Which of the following is/are CORRECT?

Let an = \((1+\frac{1}{n})^{\frac{n}{2}}\) be the n^𝑡ℎ term of the sequence 〈a_n 〉, n = 1, 2, 3, …. Then which one of the following is NOT CORRECT?

Let 𝑀 and 𝑁 be events defined on the sample space 𝑆. If 𝑃(𝑀) = \(\frac{1}{3}\) and 𝑃(𝑁^𝑐 ) = \(\frac{1}{4}\) then which one of the following is necessarily CORRECT?