DSE 2013 question paper

All 60 questions from the DSE 2013 Delhi School of Economics MA entrance paper. Open any question for the worked solution.

1. Q1Starting from a stationary position, Sonia ran 100 meters in 20 seconds. Assuming that her distance from the starting point is a continuous and…
2. Q2Suppose f:ℜ→ℜ. If f is differentiable, f(3)=2, and 3≤ f′(x)≤ 4 for all x, then it must be that f(5) lies in the following interval:
3. Q3The function defined by f(x)=x(x-10)(x-20)(x-30) has critical points (points where f′(x)=0):
4. Q4The area of the region bounded above by f(x)=x²+1 and below by g(x)=x-6 on the interval [-1,3] is:
5. Q5lim_(x→ 3)((x²-5x-2)/(x-2))^(1/3) equals:
6. Q6Consider an individual A with utility u(x)=10√x, where x is money available. She has Rs 100. She can buy a lottery costing Rs 51 that pays Rs 351…
7. Q7Two goods are imperfect substitutes with demands D₁=a-p₁+bp₂ and D₂=a-p₂+bp₁, where a>0, 0<b<1; each is produced at cost c per unit. Find the…
8. Q8Two goods are imperfect substitutes with demands D₁=a-p₁+bp₂ and D₂=a-p₂+bp₁, a>0, 0<b<1, cost c per unit. Find the equilibrium prices when both…
9. Q9Table 1 (Datt and Ravallion, EPW 2010): Rate of change of the Headcount Ratio H (% p.a.) is -1.1 pre-1991 and -2.4 post-1991; the rate of population…
10. Q10Table 2 (Datt and Ravallion, EPW 2010): the elasticity E of H with respect to mean consumption C is, pre-1991, -1.6 (NSS) and -1.0 (NAS); post-1991…
11. Q11If two balanced dice are rolled, the sum of dots obtained is even with probability:
12. Q12A population is growing at the instantaneous growth rate of 1.5 per cent. The time taken (in years) for it to double is approximately:
13. Q13A linear regression model y=α+β x+ε is estimated using OLS. It turns out that the estimated β̂ equals zero. This implies that:
14. Q14An analyst has data on wages for 100 individuals. The arithmetic mean of the log of wages is the same as:
15. Q15A 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…
16. Q16Exchange rate overshooting occurs:
17. Q17In an open economy with a system of flexible exchange rates and perfect capital mobility, an expansionary monetary policy:
18. Q18The short-run aggregate supply curve is upward sloping because:
19. Q19The term 'seignorage' is associated with:
20. Q20If money demand is stable, an open market purchase of government securities by the central bank will:
21. Q21The function defined by f(x)=x⁵+7x³+13x-18:
22. Q22The function f(x)=1/4x⁴-1/2x³-3x²+6 is:
23. Q23Consider f(x)=9/2x^(2/3)-3/5x^(5/3) for all x in [-1,5]. f(5) is approximately 4.386. f attains a maximum on [-1,5] at:
24. Q24Consider f(x)=x⁶+5x⁴+2 for all x≥ 0. The derivative of its inverse function evaluated at f(x)=8, that is (f⁻¹)′(8), equals:
25. Q25Consider f:ℜ²→ℜ³ defined by f(x,y)=(x+2y, x-y, -2x+3y), and g:ℜ²→ℜ² defined by g(x,y)=(x+1, y+2). Then:
26. Q26A six meter long string is cut into two pieces. The first piece, of length x, is used to make a circle; the second, of length 6-x, to make a square.…
27. Q27The repeated nonterminating decimal 0.272727…:
28. Q28Three players 1, 2, 3 allocate 9 indivisible coins. Player 1 proposes (x₁,x₂,x₃); players 2 and 3 vote Y or N. Two Y votes implement it; two N…
29. Q29Three players 1, 2, 3 allocate 9 indivisible coins. Player 1 proposes (x₁,x₂,x₃); players 2 and 3 vote Y or N. Two Y votes implement it; two N…
30. Q30Three players 1, 2, 3 allocate 9 indivisible coins. Player 1 proposes (x₁,x₂,x₃); players 2 and 3 vote Y or N. Two Y votes implement it; two N…
31. Q31Utility of a consumer is u(x₁,x₂)=min {x₁,x₂}. His income is M, and the price of good 2 is 1. There are two available price schemes for good 1: (i)…
32. Q32An individual lives for two periods, consuming only rice. In period 2 she costlessly produces 1 unit of rice; in period 1 she produces nothing but…
33. Q33An individual lives for two periods, consuming only rice. In period 2 she costlessly produces 1 unit of rice; in period 1 she produces nothing but…
34. Q34In a two-person two-good exchange economy, agents are A and B and goods are 1 and 2, with utilities u_A(x₁,x₂)=α x₁+x₂ and u_B(y₁,y₂)=y₁y₂. There…
35. Q35In a two-person two-good exchange economy, agents are A and B and goods are 1 and 2, with utilities u_A(x₁,x₂)=α x₁+x₂ and u_B(y₁,y₂)=y₁y₂. There…
36. Q36A basic good (a car) is produced by a monopolist at no cost; a complementary good (car audio) is produced competitively at cost c per unit. Let p be…
37. Q37A basic good (a car) is produced by a monopolist at no cost; a complementary good (car audio) is produced competitively at cost c per unit. Let p be…
38. Q38Suppose a city can be described by the interval [0,1]. Only two citizens, A and B, live in this city at different locations, A at 0.2 and B at 0.7.…
39. Q39In an exchange economy with agents 1 and 2 and goods x and y, agent 1 lexicographically prefers good x (of two bundles she strictly prefers the one…
40. Q40In an exchange economy with agents 1 and 2 and goods x and y, agent 1 lexicographically prefers good y and agent 2 lexicographically prefers good x.…
41. Q41Consider two disjoint events A and B in a sample space S. Which of the following is correct?
42. Q42A bowl contains 5 chips, 3 marked $1 and 2 marked $4. A player draws 2 chips at random and is paid the sum of the values of the chips. The player's…
43. Q43Consider two income distributions in a 10-person society. A:(1000,1000,1000,1000,1000,1000,1000,2000,2000,2000) and…
44. Q44A club consists of 5 men and 5 women. A 5-member committee of 2 men and 3 women has to be constituted. Suppose Mrs. F refuses to work with Mr. M.…
45. Q45You are an editor of a magazine and every day you get two letters from correspondents, each as likely to be from a male as a female. The postman…
46. Q46On an average, a waiter gets no tip from two of his customers on Saturdays. What is the probability that on next Saturday, he will get no tip from…
47. Q47A linear regression model y=α+β x+ε is estimated using OLS. It turns out that the estimated R² equals zero. This implies that:
48. Q48Using ordinary least squares, a market analyst estimates the demand function log X=α+βlog P+ε, where X is output and P is price. In another…
49. Q49A linear regression model y=α+β x+ε is estimated using OLS, but the variance of the error term is not constant and in fact varies directly with…
50. Q50Suppose the distribution function F(x) of a random variable X is rising in the interval [a,b) and horizontal in the interval [b,c]. Which of the…
51. Q51Consider an open economy simple Keynesian model with autonomous investment I. People save a constant proportion s of disposable income and consume…
52. Q52Consider an open economy simple Keynesian model with autonomous investment I. People save a constant proportion s of disposable income and consume…
53. Q53Consider an open economy simple Keynesian model with autonomous investment I. People save a constant proportion s of disposable income and consume…
54. Q54Suppose in an economy banks maintain a cash reserve ratio of 20%. People hold 25% of their money in currency form and the rest in demand deposits.…
55. Q55Consider the standard IS-LM framework with exogenous money supply. Now suppose the government introduces an endogenous money supply rule such that…
56. Q56In an economy, aggregate output is produced from capital K and labour L via Yₜ=α Kₜ+β Lₜ, with α,β>0. Both factors are fully employed; each worker…
57. Q57In an economy, aggregate output is produced from capital K and labour L via Yₜ=α Kₜ+β Lₜ, with α,β>0. Both factors are fully employed; each worker…
58. Q58In an economy, aggregate output is produced from capital K and labour L via Yₜ=α Kₜ+β Lₜ, with α,β>0. Both factors are fully employed; each worker…
59. Q59In an economy, aggregate output is produced from capital K and labour L via Yₜ=α Kₜ+β Lₜ, with α,β>0. Both factors are fully employed; each worker…
60. Q60In an economy, aggregate output is produced from capital K and labour L via Yₜ=α Kₜ+β Lₜ, with α,β>0. Both factors are fully employed; each worker…