DSE 2009 question paper

All 59 questions from the DSE 2009 Delhi School of Economics MA entrance paper. Open any question for the worked solution.

Q1There are 4 married couples in a club. A 3-member committee must be formed from among them, such that no married couple is part of the committee.…
Q2For any sets E and F, E-F={x∈ E| x∉ F}, with ∪ and ∩ the union and intersection. Consider for sets A,B,C: (i) A-(B∪ C)=(A-B)∪(A-C); (ii) A-(B∪…
Q3∫_(1.96)^∞ e^(-x²/2) dx is approximately
Q4Consider maximizing f(x,y)=x²-y² subject to the constraint x+y=1, where x and y are real numbers. This problem has
Q5Suppose P(x) and Q(x) are real polynomials of degree m and k respectively, where both m and k are less than or equal to the positive integer n.…
Q6There are three alternative definitions of a consistent estimator. I: An estimator is consistent if its probability limit equals its true parameter…
Q7Given the data Σ XY=350, Σ X=50, Σ Y=60, N=10, V(X)=4, V(Y)=9, where V(·) is the population variance. The correlation coefficient between X and Y…
Q8In a surprise check in a local bus, 20 passengers were caught without tickets. The sum of squares and the population standard deviation of the…
Q9In a linear regression of Y on X, changing the units of measurement of the Y variable will affect all of the following except:
Q10A fair die has numbers 1,2,3,4,5 and 6 on its sides. It is tossed once. I win Rs. 1 if an odd number shows up; otherwise I lose Rs. 1. Let X be the…
Q11Your budget is such that if you spend your entire income on two goods, x and y, you can afford either 4 units of x and 6 units of y, or 12 units of…
Q12The demand function for lemonade is Q_d=100-p, and the supply function is Qₛ=10+2p, where p is the price in rupees. The government levies a sales…
Q13There are only two price taking firms in a market. Their cost functions are C₁=x₁² and C₂=2x₂², where xᵢ is the output of the i -th firm. Market…
Q14A monopoly faces the demand curve P=8-Q. The monopoly has a constant unit cost equal to 5 for Q≤ 2 and a constant unit cost equal to 3 for Q>2. Its…
Q15A firm has the production function y=min {L+2K, 2L+K}, where y is output and L,K are labour and capital. If the input price of L is Rupee 1 and the…
Q16The opportunity cost of holding money (that yields zero nominal return) vis-a-vis some interest bearing bond is:
Q17In the IS-LM framework, an increase in the expected rate of inflation results in
Q18When the nominal wage rate is rigid, the aggregate supply schedule (in the output-price space) is:
Q19In the IS-LM framework with an external sector (so the IS equation now includes a net export term), an appreciation of the (real) exchange rate
Q20According to the Baumol-Tobin Model, if income rises by ten percent, the transactions demand for money should rise by
Q21Consider the following statements: (i) 5⁴⁴>4⁵³; (ii) 2¹⁰⁰+3¹⁰⁰<4¹⁰⁰.
Q22The WOW Language has only 2 letters, O and W, and obeys: (i) deleting successive letters WO from any word with more than 2 letters gives another…
Q23Consider the system in unknowns x and y: ax+y=a² and x+ay=1. Sets of all values of a for which this system has (i) no solution, (ii) multiple…
Q24Consider the system: x-y+z=1, 3x+z=3, 5x-2y+3z=5. This system has
Q25Consider the function f(x)=x²sin (1/x) for x≠ 0 and f(0)=0. Then the following is true about the derivative of f:
Q26For a set S, let S²=S× S. A binary relation R on S is a subset of S². R is transitive if (x,y)∈ R and (y,z)∈ R imply (x,z)∈ R. R is negatively…
Q27A function f(x₁,x₂,T)=(y₁,y₂) is defined as follows, where x₁,x₂,T are non-negative reals and x₁+x₂≥ T: y₁=min (α,x₁), y₂=min (α,x₂) such that…
Q28A function f is defined by f(x)=x² if x≤ c and f(x)=ax+b if x>c, where a,b,c are constants. Find values of a and b such that f′(c) exists.
Q29f(c)=max_(2x+y=c, x≥ 0, y≥ 0)(x+2y). Find f′(c).
Q30There are 3 persons A, B and C. One is a Truth-teller (always truthful), one a Liar (always lies), and the third a Normal person (sometimes lies…
Q31The nine digits 1,2,…,9 are arranged in random order to form a nine digit number, using each digit exactly once. Find the probability that 1, 2 and…
Q32In a survey of 102 Timarpur residents in 2009, the average income was found to be Rs. 4635 per month. Previous studies show the population variance…
Q33Let X denote the absolute value of the difference between the numbers obtained when two dice are tossed. The expectation of X is:
Q34Let Y denote the number of heads obtained when 3 coins are tossed. The variance of Y² is:
Q35A company has 100 employees, 40 men and 60 women. There are 6 male executives. How many female executives should there be for gender and rank to be…
Q36Consider two events A and B with Pr (A)=0.4 and Pr (B)=0.7. The maximum and minimum values of Pr (A∩ B) respectively are:
Q37Jai and Vijay are taking an exam in statistics with grades A, B, C. Pr (Jai gets B)=0.3, Pr (Vijay gets B)=0.4, and Pr (neither gets an A, but at…
Q38You have been told that a family has two children and one of these is a daughter. What is the probability that the other child is also a daughter?
Q39Suppose least squares is used to fit yᵢ=β₁+β₂xᵢ+εᵢ, with not all x 's identical. Assumptions: (1) E(εᵢ)=0; (2) Cov(xᵢ,εᵢ)=0; (3) homoskedasticity…
Q40When are the least-squares estimators 'best' (lowest variance) of any unbiased estimators?
Q41A consumer spends an income of Rs. 100 on two goods, dosas (x) and pizzas (y), fractions allowed, with utility U=e^(x²+y²). The price of a dosa is…
Q42Romeo and Juliet have 96 chocolates to divide. Romeo's utility is U=R⁸J⁴ and Juliet's is U=R⁴J⁸, where R is Romeo's consumption and J is Juliet's…
Q43A consumer spends Rs. 100 on only two goods, A and B, with non-satiation. The price of B is fixed at Rs. 20. When the price of A is Rs. 10, the…
Q44'Suraksha' is the sole producer and supplier of security systems and the sole employer of locksmiths. Demand for security systems is D(p)=100-p.…
Q45If the government sets the minimum wage at 70, how many locksmiths will Suraksha employ?
Q46A typical graduate student lives in a two-good world, books (x) and movies (y), with utility u(x,y)=x^(1/3)y^(4/3). Prices of books and movies are…
Q47(Same student, u=x^(1/3)y^(4/3), prices 50 and 10.) Scheme 2: 1000 as scholarship and one movie free for each book purchased. The optimal…
Q48Let R, I, P denote the weak preference, indifference and strict preference relations over X={x,y,z}. R satisfies Quasitransitivity iff for all…
Q49Consider an exchange economy with consumers A and B and goods x,y; total x=4, total y=2, optimally distributed. A's utility is…
Q51An economy is described by a goods-market equilibrium Y=C(Y)+I(r)+G+NX(Y,e) and a money-market equilibrium M/P=L(Y,r), with C=C̄+σ(Y-T), T=τ Y…
Q52(Same model.) An increase in r̄ shifts
Q53(Same model.) An increase in P̄ results in
Q54(Same model.) If the government arbitrarily fixes the real exchange rate at some ē,
Q55A fall in the interest rate
Q56An increase in the rate of depreciation, according to the neoclassical theory of investment, will
Q57An increase in the saving rate in the Solow model
Q58The 'golden rule of accumulation' is the
Q59At the 'golden rule of accumulation'
Q60Consider three definitions for a country's current account surplus. Which are correct? (i) equal to its trade balance plus net income from abroad…