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

Which of the following deficits indicates the true current fiscal position of the Indian Economy?

Which of the following functions is/are homogeneous?

An individual faces an uncertain prospect, where wealth could be Rs. 10 Lakh with probability 0.75 and Rs. 7 Lakh with probability 0.25.
Let the utility function be U(w) = w³. Then the individual will buy full insurance by paying a premium of Rs. _____ Lakh (round off to 2 decimal places).

Let ƒ be defined by $f(x) = |x| + |cos({\frac{\pi }{2} - x }), x \, \, \epsilon \, \,(-\frac{\pi }{2},\frac{\pi }{2}).$ Then

The technical change in the endogenous growth model is endogenized by

Let f: [0,∞) → \(\R\) be a function defined by \(f(x)=\frac{x+1}{x+2}\) for all \(x\isin\R\). Then f is

Let the consumption function, tax function, and income identity be given by C = C₀+b(Y-T), T = T₀+tY, and Y=C+I₀+ G₀, respectively, where C₀, I₀, G₀, and T₀ are autonomous consumption, investment, government expenditure, and tax, respectively. If b = 0.75 and t = 0.1, then an increase in G₀ by Rs. 20 million will increase Y by Rs. ______ million (round off to 2 decimal places).

Let the function \(f: R^2⇢R\)  be \(f(x, y) = \frac{xy^2}{ x^3+  2xy + y^3}\,\,  f(0, 0) = 0.\) Then

Let the linear programming problem be
Maximize Z = - 0.2x₁ + x₂
subject to 2x₁ + 5x₂ ≤ 70,
x₁ + x₂ ≤ 20,
x₁, x₂ ≥ 0.
If x₁ = a and x₂ = b is the optimal solution, then a+b=______ (in integer).

Assume that the cost function for the i^th firm in an industry is given by
C_i = 0.25\(q^2_i\) + 2q_i + 5, i = 1, 2, ..., 150,
where C_i and q_i are cost and output for the i^th firm, respectively.
Let the aggregate inverse demand function be P = 10-0.01Q, where P is the unit price and Q is the aggregate output.
Assuming perfect competition, the equilibrium quantity is _____ (in integer).

Let the production function be Q = \(\sqrt{L^2 + K^2}\) the unit price of labour (L) and capital (K) be Rs. 30 and Rs. 40, respectively, and the total cost be Rs. 580. Then the maximum value of Q subject to the cost constraint is ______ (round off to 2 decimal places).

Let the system of equations be αu+w=0, u+αν =0, v+αw=0, where a ∈ ℜ. Then the system has infinite solutions if a =_____ (in integer).

Choose the option that represents the original linear programming problem based on the initial simplex tableau given below, where \(S_i\) represents slack/surplus variables and \(A_i\) represents the artificial variables corresponding to the \(i^{th}\)constraint: 

Let \(x^3+3y^2=4\) for all \(x,y\isin\R,\) \(y'=\frac{dy}{dx}\) and \(y''=\frac{d^2y}{dx^2}\). Then

Let \(X \sim N(\mu X, \sigma _X ^2)\) and \(Y \sim N(\mu _y, \sigma _y ^2)\) Which of the following is/are NOT correct?

ACD Bank holds a total deposit of Rs. 256412. To expand the money supply in the economy during the COVID-19 pandemic period, the Reserve Bank of India reduces the cash reserve ratio (CRR) from 4.5% to 3.5%. Due to this policy change, the additional money supply generated by ACD Bank is Rs. ____ (in integer).

From the following, who first examined the close negative relationship between the unemployment rate and the output ratio?

Match List I with List II and choose the CORRECT option.

List I		List II
a.	Second Five Year Plan (1956-61)	i.	Towards Faster and More Inclusive Growth
b.	Fourth Five Year Plan (1969-74)	ii.	Removal of Poverty and Attainment of Self-reliance
c.	Fifth Five Year Plan (1974-79)	iii.	Rapid Industrialization-Heavy and Basic Industries
d.	Eleventh Five Year Plan (2007-12)	iv.	Family Planning Programmes

Given the following information related to product and money markets,
\(\text{Product Market}\\C = 300 +0.8(Y – T)\\T = 200 +0.2(Y)\\I_0 = 300; G_o = 400\)           \(\text{Money Market}\\\frac{M_0}P=0.4Y-200i\\M_0=900; P = 1 (Fixed)\)
where Y Income, C = Consumption, T = Tax, I₀ = Autonomous Investment, G₀ = Autonomous Government Expenditure, M₀ = Nominal Money Demand, P = Price, and i = Interest Rate.
The equilibrium level of interest rate (in %) is ______ (round off to 2 decimal places)

Matching List I and List II, choose the CORRECT option(s).

List I	List II
a. Bombay Plan	i. J. P. Narayan
b. People's Plan	ii. J. R. D. Tata
c. Sarvodaya Plan	iii. M. N. Roy

Given the production function Q = 6√L and the supply of labour L = √w, where L and w denote the number of labours and wage rate, respectively. If the unit price of the product is Rs. 243, then the profit maximizing value of w is Rs. _____ (in integer).

Monthly per capita consumption expenditure (MPCE) of 10 households in a region is given below.

Households	H1	H2	H3	H4	H5	H6	H7	H8	H9	H10
MPCE(in Rs.)	2800	3000	1200	3500	1400	2500	4000	1000	900	1300

Assuming the poverty cutoff (Z) of MPCE to be Rs. 2000, the squared poverty gap ratio is _______(round off to 3 decimal places)

If \(\int t\log(1+\frac{2}{t})dt=g(t)(\frac{t^2}{2}-2)+f(t)\frac{t^2}{2}+Kt+C\), where C is an arbitrary constant, then 2K is ______ (in integer).

Suppose that one million unemployed persons in a country are receiving Rs. 6000 per month per person as an unemployment allowance. If the government, instead of paying unemployment allowance, hires all of them at the same amount (Rs. 6000 per month per person) and engages them in digging the pits and filling the same pits. What will be the effect on GDP?

Suppose that per capita GDP of India and USA are growing at annual average rates of 8.8% and 1.8%, respectively. Further, consider that in 2019-20, per capita GDP of USA was USD 41099 and per capita GDP of India was USD 1570. Assuming that the two countries continue to grow at the above rates, India's per capita GDP will be equal to the per capita GDP of USA in _____ years (round off to 2 decimal places).