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Questions › DSE › DSE 2019

DSE 2019 question paper

All 50 questions from the DSE 2019 Delhi School of Economics MA entrance paper. Open any question for the worked solution.

  1. Q1The range of the function f:ℜ→ℜ defined by f(x)=(x²+x+2)/(x²+x+1) is
  2. Q2Data from a random sample of 107 home sales in 2003 yielded the regression P̂=119.2+0.485 BD+23.4 BA+0.156 HS+0.002 PS+0.090 A-35.6 PC, where P is…
  3. Q3The maximum value attained by the function f(x)=x³-x²-x-1 on the set S={x| x²-x-2≤ 0} occurs at
  4. Q4A random variable X has a standard normal distribution. What is the closest guess to the probability that X lies in the interval [2,3]?
  5. Q5Consider utility functions u₁(x,y)={ 2x if y/x>2; max {x,y} if y/x∈[1/2,2]; 2y if y/x<1/2 } and u₂(x,y)={ 2x if y/x>2; x+y if y/x∈[1/2,2]; 2y if…
  6. Q6lim_(x→∞)((x²-x+1)/(x+1)-c₁x-c₂)=-5. So, it must be that (c₁,c₂) equals
  7. Q7The efficiency wage theory argues that
  8. Q8According to the theory of comparative advantage, countries gain from trade because
  9. Q9In the 2-factor, 2-good Heckscher-Ohlin model, the two countries differ in
  10. Q10The line y=2x+5 is tangent to a circle with equation x²+y²+16x+12y+c=0, at point P. So, P equals
  11. Q11The random variable X denotes the number of successes in a sequence of independent trials, each with probability p of success. Let X̄ denote the…
  12. Q12Scenario 2: Trader 1 is endowed with 100 identical Left shoes. Trader 2 is endowed with 99 identical Right shoes. Each trader's utility equals the…
  13. Q13A family has two children and it is known that at least one is a girl. What is the probability that both are girls given that at least one is a girl?
  14. Q14It is known that there is a rational number between any two distinct irrational numbers. Consider a continuous function f:ℜ→ℜ such that f(x)=sin x…
  15. Q15Scenario 2: Trader 1 is endowed with 100 identical Left shoes. Trader 2 is endowed with 99 identical Right shoes. Each trader's utility equals the…
  16. Q16Assume the aggregate production of an economy is Yₜ=√(KₜLₜ), with Kₜ₊₁=(1-δ)Kₜ+Iₜ, Sₜ=sYₜ and Lₜ=L (notation as in the Solow model with constant…
  17. Q17Consider a function f:ℜ²→ℜ. Suppose that for every p∈ℜ² there exists x(p)∈ℜ² such that f(x(p))≥ 1 and p· x(p)≤ p· y for every y∈ℜ² with f(y)≥ 1.…
  18. Q18Given nonempty subsets Y₁,…,Yₙ of ℜ², let Y*={Σⱼ₌₁ⁿ yⱼ: y₁∈ Y₁,…,yₙ∈ Yₙ}. Given p∈ℜ² and a nonempty set Y⊂ℜ², let v(p,Y)=sup {p· y: y∈ Y}. Then, for…
  19. Q19In a simple open economy framework, an increase in government spending leads to:
  20. Q20The matrix Q=PAPᵀ, where Pᵀ is the transpose of P, and P=[√3/2 1/2; -1/2 √3/2], A=[1 1; 0 1]. Then PᵀQ¹²P equals:
  21. Q21Nitin is a stamp collector and consumes only stamps and cheese sandwiches. His utility function is u(s,c)=s+log c. If Nitin is at a point where he…
  22. Q22A consumer lives for two periods 1 and 2. Lifetime utility is U=u(c₁)+u(c₂)/(1+ρ). She earns w₁,w₂ and consumption satisfies…
  23. Q23Consider the set of two equations: (2x)^(ln 2)=(3y)^(ln 3) and 3^(ln x)=2^(ln y). Suppose a pair (x,y) is a solution to this set of equations. Then…
  24. Q24The price-setting relation gives the real wage as W/P=A/(1+m) (technology A, mark-up m). The wage-setting relation gives W/P=A(1-u) (productivity A…
  25. Q25Your budget is such that if you spend your entire income, you can afford either 4 units of good x and 6 units of good y, or 12 units of good x and 2…
  26. Q26Let A=[1 1; 1 3]. Then A⁴-4A³+2A²+A equals:
  27. Q27Scenario 3: Data from a random sample of 107 home sales in 2003 yielded the regression P̂=119.2+0.485 BD+23.4 BA+0.156 HS+0.002 PS+0.090 A-35.6 PC…
  28. Q28Consider a small open economy. If there is a positive productivity shock in the country, how will the domestic capital market be affected?
  29. Q29Functions f,g from ℜ to ℜ are defined by: f(x)=0 if x is rational and f(x)=x if x is irrational; g(x)=0 if x is irrational and g(x)=x if x is…
  30. Q30Let ‖·‖ₙ and ‖·‖ₘ be norms on ℜⁿ and ℜ^m respectively. Let L be the space of linear transformations from ℜⁿ to ℜ^m. Then:
  31. Q31Scenario 2: Trader 1 is endowed with 100 identical Left shoes. Trader 2 is endowed with 99 identical Right shoes. Each trader's utility equals the…
  32. Q32Scenario 3: Data from a random sample of 107 home sales in 2003 yielded the regression P̂=119.2+0.485 BD+23.4 BA+0.156 HS+0.002 PS+0.090 A-35.6 PC…
  33. Q33Suppose that the mark-up over cost is 20% for a representative firm in an economy with labour being the single factor; and the wage-setting equation…
  34. Q34You have a single draw from a Bernoulli distribution. The maximum likelihood estimate of the probability of success p is:
  35. Q35Scenario 3: Data from a random sample of 107 home sales in 2003 yielded the regression P̂=119.2+0.485 BD+23.4 BA+0.156 HS+0.002 PS+0.090 A-35.6 PC…
  36. Q36What is the money demand function when the utility of money for the representative household is U(Y,M/P)=0.5ln Y+0.5ln (M/P) (i represents the…
  37. Q37Scenario 3: Data from a random sample of 107 home sales in 2003 yielded the regression P̂=119.2+0.485 BD+23.4 BA+0.156 HS+0.002 PS+0.090 A-35.6 PC…
  38. Q38Let A=[1 0 0; 2 1 0; 3 2 1] and B₁,B₂,B₃ be three 3× 1 column vectors such that AB₁=[1; 0; 0], AB₂=[2; 3; 0], AB₃=[2; 3; 1]. Let B be the 3× 3…
  39. Q39Scenario 3: Data from a random sample of 107 home sales in 2003 yielded the regression P̂=119.2+0.485 BD+23.4 BA+0.156 HS+0.002 PS+0.090 A-35.6 PC…
  40. Q40A random number X, uniformly distributed on [0,1], divides [0,1] into 2 segments of lengths X and (1-X). Let R be the ratio of the smaller to the…
  41. Q41The function f(x) is twice differentiable, and f(2)=4, f(3)=9, f(4)=16. Then, it must be that:
  42. Q42If the marginal propensity to save is 0.3 and the marginal propensity to import is 0.1, and the government increases expenditures by Rs. 10 billion…
  43. Q43Under a floating exchange rate regime, following an expansion in the money supply, monetary authorities will:
  44. Q44In a roll of two fair dice, X is the number on the first die and Y is the number on the second die. Which of the following statements is true?
  45. Q45The formula for the effective tariff rate is e=(n-ab)/(1-a), where e is the effective rate of protection, n is the nominal tariff rate on the final…
  46. Q46Suppose that in the Solow Model of an economy with some positive savings rate, population growth rate, and rate of depreciation, k* is the steady…
  47. Q47A random variable has a Uniform distribution on the interval [-1,1]. The probability density function of X conditional on X>0.3 is given by:
  48. Q48The set (0,∞) can be expressed as:
  49. Q49What is the probability that at least one 6 appears when 6 fair dice are rolled?
  50. Q50Scenario 1: Consider utility functions u₁(x,y)=2x if y/x>2, max {x,y} if y/x∈[1/2,2], and 2y if y/x<1/2; and u₂(x,y)=2x if y/x>2, x+y if…