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Delhi University Entrance Test (DUET) 2020 Previous Year Question Paper With Answer Key

This post was last modified on 27 December 2020

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Topic:- ECO MA S2

Consider independently and identically distributed random variables X1, ..., Xn with values in [0, 2]. Each of these random variables is uniformly distributed on [0, 2]. If Y = max{X1,..., Xn}, then the mean of Y is [Question ID = 5844]
1. [n/(n + 1)]2 [Option ID = 23370]
2. n/2(n + 1) [Option ID = 23371]
3. 2n/(n + 1) [Option ID = 23372]
4. n/(n + 1) [Option ID = 23373]
Correct Answer :-
- 2n/(n + 1) [Option ID = 23372]
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 nth 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? [Question ID = 5845]
1. 1 [Option ID = 23374]
2. -1 [Option ID = 23375]
3. 3 [Option ID = 23376]
4. -3 [Option ID = 23377]
Correct Answer :-
- -1 [Option ID = 23375]

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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? [Question ID = 5846]
1. 1/3 [Option ID = 23378]
2. 2/9 [Option ID = 23379]
3. 4/9 [Option ID = 23380]
4. 7/16 [Option ID = 23381]
Correct Answer :-
- 2/9 [Option ID = 23379]
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 [Question ID = 5847]
1. mp/[1 + (m - 1)p] [Option ID = 23382]
2. mp/[1 + (1-p)m] [Option ID = 23383]
3. (1-p)/[1 + (m - 1)p] [Option ID = 23384]
4. (1-p)/[1 + (1-p)m] [Option ID = 23385]
Correct Answer :-
- mp/[1 + (m - 1)p] [Option ID = 23382]
Suppose Y is a random variable with uniform distribution on [0, 2]. The value of the cumulative distribution function of the random variable X = e^Y at x ∈ [1, e²] is [Question ID = 5848]
1. 2^-1 ln x [Option ID = 23386]
2. 4^-1 ln x - 2^-1 [Option ID = 23387]
3. ln x [Option ID = 23388]
4. ln x - 1 [Option ID = 23389]
Correct Answer :-
- 2^-1 In x [Option ID = 23386]
Consider an economy where the final commodity is produced by a single firm using labour only. The price-setting firm charges a 25% mark-up over its per unit nominal wage cost. The workers demand a real wage rate W/P = (1 - u), where u is the unemployment rate, P is the price, and W is the nominal wage rate. The natural rate of unemployment in this economy is [Question ID = 5849]
1. 20% [Option ID = 23390]
2. 17% [Option ID = 23391]
Correct Answer :-
- 20% [Option ID = 23390]
The aggregate production function of an economy is Yt = (KtLt) ^1/2. Capital grows according to Kt+1 = (1 – δ) Κt + St, where St = sYt, Lt = 1, s is the saving rate, δ is the depreciation rate and is the total population. Then, the steady-state level of consumption per capita is [Question ID = 5850]
1. ς/δ [Option ID = 23394]
2. s²/δ² [Option ID = 23395]
3. δ/ς [Option ID = 23396]
4. s(1 - s)/δ [Option ID = 23397]
Correct Answer :-
- s(1 - s)/δ [Option ID = 23397]
Consider a production technology Y = AL, where Y is output, A is productivity, and L is labour input. A firm sets its price P at a constant mark-up μ over the effective wage cost per unit of production W/A. The expected real wage rate of workers is W/Pe = A^α(1 – u)^1-α, where 0 < α < 1 and Pe is the expected price. If the price expected by workers matches the actual price level, then the effect of a rise in the level of productivity on unemployment is [Question ID = 5851]
1. positive [Option ID = 23398]
2. negative [Option ID = 23399]
3. zero [Option ID = 23400]
4. ambiguous [Option ID = 23401]
Correct Answer :-
- negative [Option ID = 23399]
A household has an endowment of 1 unit of time. The household maximises its utility u = In c + b ln(1 - l), where c denotes consumption and l ∈ [0, 1] denotes time spent working. It finances its consumption from labour income wl, where w is the market wage rate per unit of labour time. If the market wage rate goes up, then equilibrium labour supply of the household [Question ID = 5852]
1. increases [Option ID = 23402]
2. decreases [Option ID = 23403]
3. remains constant [Option ID = 23404]
4. changes in an ambiguous manner [Option ID = 23405]
Correct Answer :-
- remains constant [Option ID = 23404]

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Consider the IS-LM model with a given price level P. Investment is a decreasing function of the interest rate and savings is an increasing function of aggregate income. The demand for real money balances M/P is an increasing function of aggregate income and a decreasing function of the interest rate. The monetary authority chooses nominal money supply M so that the resulting money market equilibrium keeps the interest rate fixed at some target level. In this setup, an increase in government expenditure will cause [Question ID = 5853]
1. a rise in equilibrium output [Option ID = 23406]
2. a fall in equilibrium output [Option ID = 23407]
3. no effect on equilibrium output [Option ID = 23408]
4. an ambiguous effect on equilibrium output [Option ID = 23409]
Correct Answer :-
- a fall in equilibrium output [Option ID = 23407]
Consider the Solow growth model with a given savings ratio, a constant population growth rate, zero rate of capital depreciation, and no technical progress. Let k* be the steady-state capital-labour ratio in this economy. Suppose the economy is yet to reach the steady-state and has capital-labour ratio k₁ at time t₁ and capital-labour ratio k2 at time t2, such that t₁ < t2 and k₁ < k2 < k*. Let the associated growth rates of per capita income at time t₁ and t2 be g₁ and g2 respectively. Then, by the properties of the Solow model, [Question ID = 5854]
1. g1 < g2 [Option ID = 23410]
2. g1 > g2 [Option ID = 23411]
3. g1 = g2 [Option ID = 23412]
4. the relationship between g₁ and g2 is ambiguous [Option ID = 23413]
Correct Answer :-
- g1 > g2 [Option ID = 23411]
A consumer lives for periods 1 and 2. Given consumptions c₁ and c₂ in these periods, her utility is U = In c₁ + (1 + ρ)^-1 In c2. She earns incomes w₁ and w₂ in the two periods and her lifetime budget constraint is c₁ + (1 + r)^-1c2 = W₁ + (1 + r)^-1w2, where r is the interest rate on savings. If r > ρ, then [Question ID = 5855]
1. C1 > C2 [Option ID = 23414]
2. C1 < C2 [Option ID = 23415]
3. C₁ = C2 [Option ID = 23416]
4. The relationship between c₁ and c₂ is ambiguous [Option ID = 23417]
Correct Answer :-
- C1 < C2 [Option ID = 23415]
A consumer lives for periods 1 and 2. Her lifetime utility function is U(C1, C2) = (C₁^γ+C₂^γ)^1/γ where 0 < γ < 1 and ci is consumption in period i. The elasticity of substitution between consumption in period 1 and consumption in period 2 is [Question ID = 5856]
1. 1 + γ [Option ID = 23418]
2. 1 - γ [Option ID = 23419]
3. 1/(1 + γ) [Option ID = 23420]
4. 1/(1 – γ) [Option ID = 23421]
Correct Answer :-
- 1/(1 – γ) [Option ID = 23421]
Two equally skilled tennis players are to play a best-of-seven match, i.e., the first to win four games will win the match. The two are equally likely to win any of the games in the match. The probability that the match will end in 6 games is [Question ID = 5857]
1. less than the probability that it will end in 7 games [Option ID = 23422]
2. equal to the probability that it will end in 7 games [Option ID = 23423]
3. greater than the probability that it will end in 7 games [Option ID = 23424]
4. None of these [Option ID = 23425]
Correct Answer :-
- equal to the probability that it will end in 7 games [Option ID = 23423]

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Let X and Y be jointly normally distributed, i.e., (X,Y)~ Ν(μ_x, μ_y, σ_x², σ_y², ρ) If σ_x² = σ_y² and 0<ρ<1, then [Question ID = 5858]
1. the OLS regression of Y on X will yield a slope that is less than unity, and that of X on Y will yield a slope greater than unity [Option ID = 23426]
2. the OLS regression of Y on X will yield a slope that is less than unity, and that of X on Y will yield a slope less than unity [Option ID = 23427]
3. the OLS regression of Y on X will yield a slope that is greater than unity, and that of X on Y will yield a slope less than unity [Option ID = 23428]
4. it is not possible to draw conclusions about the magnitude of the slope with the given information [Option ID = 23429]
Correct Answer :-
- the OLS regression of Y on X will yield a slope that is less than unity, and that of X on Y will yield a slope less than unity [Option ID = 23427]
Let ¬ denote the negation of a statement. Consider a set X and a binary relation > on X. Relation > is said to be irreflexive if ¬x > x for every x ∈ X. Relation > is said to be transitive if, for all x, y, z ∈ X, x > y and y > z implies x > z. If > is asymmetric (i.e., for all x, y ∈ X, x > y implies ¬y > x) and negatively transitive (i.e., for all x, y, z ∈ X, x > y implies x > z, or z > y, or both), then > is [Question ID = 5859]
1. irreflexive, but not transitive [Option ID = 23430]
2. transitive, but not irreflexive [Option ID = 23431]
3. irreflexive and transitive [Option ID = 23432]
4. neither transitive, nor irreflexive [Option ID = 23433]
Correct Answer :-
- irreflexive and transitive [Option ID = 23432]
Let ¬ denote the negation of a statement. Consider a set X and a binary relation > on X. For all x, y ∈ X, we say x > y if and only if ¬y> x. Relation > is said to be total if, for all x, y ∈ X, x > y implies y > x. If > is asymmetric (i.e., for all x, y ∈ X, x > y implies ¬y > x) and negatively transitive (i.e., for all x, y, z ∈ X, x > y implies x > z, or z > y, or both), then > [Question ID = 5860]
1. is not total [Option ID = 23434]
2. is total [Option ID = 23435]
3. is not total over a nonempty subset of X [Option ID = 23437]
Correct Answer :-
- is total [Option ID = 23435]
Let ¬ denote the negation of a statement. Consider a set X and a binary relation > on X. For all x, y ∈ X, we say x > y if and only if ¬y> x. Relation is said to be transitive if, for all x, y, z ∈ X, x > y and y z implies x > z. If > is asymmetric (i.e., for all x, y ∈ X, x > y implies ¬y > x) and negatively transitive (i.e., for all x, y, z ∈ X, x > y implies x > z, or z > y, or both), then > [Question ID = 5861]
1. is not transitive over a nonempty subset of X [Option ID = 23438]
2. is not transitive [Option ID = 23439]
3. may not be transitive [Option ID = 23440]
4. is transitive [Option ID = 23441]
Correct Answer :-
- is transitive [Option ID = 23441]
Let ¬ denote the negation of a statement. Consider a set X and a binary relation > on X. For all x, y ∈ X, we say x - y if and only if x>y and ¬y > x. Relation ~ is said to be transitive if, for all x, y, z ∈ X, x~y and y~z implies x ~ z. If > is asymmetric (i.e., for all x, y ∈ X, x > y implies ¬y > x) and negatively transitive (i.e., for all x, y, z ∈ X, x > y implies x > z, or z > y, or both), then ~ [Question ID = 5862]
1. is transitive [Option ID = 23442]
2. is not transitive [Option ID = 23443]
3. may not be transitive [Option ID = 23444]
4. is not transitive over a nonempty subset of X [Option ID = 23445]
Correct Answer :-
- is transitive [Option ID = 23442]
Let ¬ denote the negation of a statement. Consider a set X and a binary relation > on X. For all x, y ∈ X, we say x~y if and only if x > y and y > x. Relation ~ is said to be symmetric if, for all x, y ∈ X, x - y implies y ~ x. If > is asymmetric (i.e., for all x, y ∈ X, x > y implies ¬y > x) and negatively transitive (i.e., for all x, y, z ∈ X, x > y implies x > z, or z > y, or both), then ~ [Question ID = 5863]
1. is symmetric [Option ID = 23446]
2. is not symmetric [Option ID = 23447]
3. may not be symmetric [Option ID = 23448]
4. is not symmetric over a nonempty subset of X [Option ID = 23449]
Consider the following game for players 1 and 2. Player 1 moves first and chooses L or R. If she chooses L, then the game ends and the payoffs are (1, 0), where the first entry is 1's payoff and the second entry is 2's payoff. If she chooses R, then 2 chooses U or D. If she chooses U, then the game ends and the payoffs are (0, 2). If she chooses D, then 1 chooses L or R. If she chooses L, then the game ends and the payoffs are (4, 0). If she chooses R, then the game ends and the payoffs are (3, 3). This game has [Question ID = 5864]
1. one Nash equilibrium in pure strategies [Option ID = 23450]
2. two Nash equilibria in pure strategies [Option ID = 23451]
3. three Nash equilibria in pure strategies [Option ID = 23452]
4. no Nash equilibria in pure strategies [Option ID = 23453]
Correct Answer :-
- two Nash equilibria in pure strategies [Option ID = 23451]

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Consider the following game for players 1 and 2. Player 1 moves first and chooses L or R. If she chooses L, then the game ends and the payoffs are (1, 0), where the first entry is 1's payoff and the second entry is 2's payoff. If she chooses R, then 2 chooses U or D. If she chooses U, then the game ends and the payoffs are (0, 2). If she chooses D, then 1 chooses L or R. If she chooses L, then the game ends and the payoffs are (4, 0). If she chooses R, then the game ends and the payoffs are (3, 3). This game has [Question ID = 5865]
1. one subgame perfect Nash equilibrium [Option ID = 23454]
2. two subgame perfect Nash equilibria [Option ID = 23455]
3. three subgame perfect Nash equilibria [Option ID = 23456]
4. no subgame perfect Nash equilibria [Option ID = 23457]
Correct Answer :-
- one subgame perfect Nash equilibrium [Option ID = 23454]
In a non-cooperative game, if a profile of strategies [Question ID = 5866]
1. is a Nash equilibrium, then it is an equilibrium in dominant strategies [Option ID = 23458]
2. is a Nash equilibrium, then it is a subgame perfect equilibrium [Option ID = 23459]
3. is a Nash equilibrium, then it is a sequential equilibrium [Option ID = 23460]
4. is an equilibrium in dominant strategies, then it is a Nash equilibrium [Option ID = 23461]
Correct Answer :-
- is an equilibrium in dominant strategies, then it is a Nash equilibrium [Option ID = 23461]
If player 1 is the row player and player 2 is the column player in games G=

L R

U a,b c,d

D e,f g,h

and G'=

L M R

U a,b a,c d

D e,f γ, δ g,h

then [Question ID = 5867]
1. 2's payoff in a Nash equilibrium of G' cannot be less than 2's payoff in a Nash equilibrium of G [Option ID = 23462]
2. 2's payoff in a Nash equilibrium of G cannot be less than 2's payoff in a Nash equilibrium of G' [Option ID = 23463]
3. 2's payoff in a Nash equilibrium of G must be equal to 2's payoff in a Nash equilibrium of G' [Option ID = 23464]
4. 2's payoff in a Nash equilibrium of G may be higher than 2's payoff in a Nash equilibrium of G' [Option ID = 23465]
Correct Answer :-
- 2's payoff in a Nash equilibrium of G may be higher than 2's payoff in a Nash equilibrium of G' [Option ID = 23465]
Consider an exchange economy with agents 1 and 2 and goods x and y. Agent 1 lexicographically prefers x to y, i.e., between two non-identical bundles of x and y, she strictly prefers the bundle with more of x, but if the bundles have the same amount of x, then she strictly prefers the bundle with more of y. Agent 2's utility function is u₂(x,y) = x + y Agent 1's endowment is (ω_x¹,ω_y¹) = (0,10) and Agent 2's endowment is (ω_x²,ω_y²) = (10,0) The set of competitive equilibrium price ratios p_x/p_y for this economy is [Question ID = 5868]
1. {1} [Option ID = 23466]
2. [0,1] [Option ID = 23467]
3. (0,1] [Option ID = 23468]
4. Ø [Option ID = 23469]
Correct Answer :-
- {1} [Option ID = 23466]
Consider an exchange economy with agents 1 and 2 and goods x and y. Agent 1 lexicographically prefers y to x, i.e., between two non-identical bundles of x and y, she strictly prefers the bundle with more of y, but if the bundles have the same amount of y, then she strictly prefers the bundle with more of x. Agent 2's utility function is u₂(x,y) = x + y Agent 1's endowment is (ω_x¹,ω_y¹) = (0,10) and Agent 2's endowment is (ω_x²,ω_y²) = (10,0) The set of competitive equilibrium price ratios p_x/p_y, for this economy is [Question ID = 5869]
1. {1} [Option ID = 23470]
2. [0,1] [Option ID = 23471]
3. (0,1] [Option ID = 23472]
4. Ø [Option ID = 23473]
Correct Answer :-
- (0,1] [Option ID = 23472]

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Consider an exchange economy with goods x and y, and agents 1 and 2, whose endowments are (ω_x¹,ω_y¹) = (0,9) and (ω_x²,ω_y²) = (10,0) respectively. The utility functions of 1 and 2 are u₁(x, y) = min{x,y} and u₂(x,y) = min{x,y} respectively. The competitive equilibrium price ratio p_x/p_y, is [Question ID = 5870]
1. 9/10 [Option ID = 23474]
2. 10/9 [Option ID = 23475]
3. 1 [Option ID = 23476]
4. 0 [Option ID = 23477]
Correct Answer :-
- 0 [Option ID = 23477]
Consider an exchange economy with goods x and y, and agents 1 and 2, whose endowments are (ω_x¹,ω_y¹) = (0,9) and (ω_x²,ω_y²) = (10,0) respectively. The utility functions of 1 and 2 are u₁(x, y) = min{x,y} and u₂(x,y) = min{x,y} respectively. The competitive equilibrium allocations are [Question ID = 5871]
1. 1 gets (x, y) and 2 gets (10 - x, 9 - y), where x ∈ [9, 10] and y = 9 [Option ID = 23479]
2. 1 gets (x, y) and 2 gets (9x, 10 y), where x ∈ [8, 9] and y = 10 [Option ID = 23480]
3. 1 gets (x, y) and 2 gets (9x, 10 y), where x = 9 and y ∈ [9, 10] [Option ID = 23481]
Correct Answer :-
- 1 gets (x, y) and 2 gets (10 - x, 9 - y), where x ∈ [9, 10] and y = 9 [Option ID = 23479]
Consider an exchange economy with goods x and y, and agents 1 and 2, whose endowments are (ω_x¹,ω_y¹) = (0,9) and (ω_x²,ω_y²) = (10,0) respectively. The utility functions of 1 and 2 are u₁(x, y) = min{x,y} and u₂(x,y) = min{x,y} respectively. The allocation that gives (10, 9) to 1 and (0,0) to 2 is [Question ID = 5872]
1. Pareto efficient but not a competitive equilibrium allocation [Option ID = 23482]
2. neither Pareto efficient nor a competitive equilibrium allocation [Option ID = 23483]
3. a competitive equilibrium allocation that is Pareto efficient [Option ID = 23484]
4. a competitive equilibrium allocation that is not Pareto efficient [Option ID = 23485]
Correct Answer :-
- a competitive equilibrium allocation that is Pareto efficient [Option ID = 23484]
Given a non-empty set C⊆ Rⁿ, for every p∈ R, let c(p) ∈ C be such that p.c(p) ≤ p.c for every c∈ C. Then, the function e: R→R given by e(p) = p.c(p) is [Question ID = 5873]
1. linear [Option ID = 23486]
2. convex [Option ID = 23487]
3. concave [Option ID = 23488]
4. quasi-convex [Option ID = 23489]
Correct Answer :-
- concave [Option ID = 23488]
Given a non-empty set C⊆ Rⁿ, for every p∈ R, let c
This download link is referred from the post: DUET Last 10 Years 2011-2021 Question Papers With Answer Key || Delhi University Entrance Test conducted by the NTA
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This post was last modified on 27 December 2020

	L	R
U	a,b	c,d
D	e,f	g,h

	L	M	R
U	a,b	a,c	d
D	e,f	γ, δ	g,h

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