DSE 2016 question paper

All 39 questions from the DSE 2016 Delhi School of Economics MA entrance paper. Open any question for the worked solution.

Q1If the following equation is estimated using OLS, and a 95% confidence interval for β₁ is constructed, then which of the following is true?
Q2What term would best describe the shape of the given boxplot? [Figure: a horizontal boxplot on a data axis running 0 to 3, with minimum ≈ 0.1, first… · diagram
Q3The vitamin content of a particular brand of vitamin supplement pills is normally distributed with mean 490 mg and standard deviation 12 mg. What is…
Q4A sample of 100 cows is drawn to estimate the mean weight of a large herd of cattle. If the standard deviation of the sample is 100 kg, what is the…
Q5Recent studies suggest that migration to Indian cities from rural regions (MIG) can be explained by Quality of life (QL), state income as a ratio of…
Q6Consider the following estimated regression relating expenditures on Food (Yᵢ) to Income (Xᵢ): Ŷᵢ=145+0.3Xᵢ-0.1(Xᵢ-Xᵢ*)Dᵢ, where i denotes the…
Q7The parameters of the following multiple regression model have been estimated using OLS: Y=β₁+β₂X₂+β₃X₃+ϵ. Denote the estimated residuals from this…
Q8In the multiple regression model with 4 explanatory variables, with standard assumptions, estimated using ordinary least squares, all the…
Q9Instead of estimating a true cost function, which is described as a quadratic, where costs are regressed on an intercept, output and a quadratic…
Q10Using data on class size (CS) and average test percentage (TP) from 101 classes, the following OLS regression is estimated: T̂P̂=96.4-1.12 CS.…
Q11In the OLS regression Yᵢ=β₁+β₂Xᵢ+uᵢ, suppose the coefficient of determination is estimated to be 0.6. We now transform the variables such that…
Q12The OLS regression of infant birth weight (BWT) on the mother's age (AGE) and years of mother's education (EDU) is: B̂ŴT̂=2600+2.3 AGE+26 EDU, with…
Q13If f:ℝ→ℝ is a continuous function (ℝ is the set of real numbers) and E is an open subset of ℝ, then the set {x∈ℝ| f(x)∈ E} is necessarily
Q14If X is an n× n non-singular matrix, such that XXᵀ=XᵀX (Xᵀ denotes the transpose of X). Let Y=X⁻¹Xᵀ where X⁻¹ denotes the inverse of X. Then YYᵀ is…
Q15Suppose that g(x) is a twice differentiable function and g(1)=1; g(2)=4; g(3)=9. Which of the following is necessarily true? (First and second…
Q16Consider f:ℝ→ℝ defined by f(x)=Σᵢ₌₁¹¹|x-aᵢ| for all x∈ℝ, where a₁<…<a₁₁. This function has a minimum when x equals:
Q17Consider the set {x,y∈ℝ₊×ℝ| y≤ln (x)-e^x}. This set is
Q18A school with n students has m clubs to which they can belong, and students are allowed to be members of multiple clubs. It is known that (I) Each…
Q19Let n>1, and let S be the set of all n× n matrices whose entries are all chosen from the set {0,1}. Then the sum of the determinants of all these…
Q20g:ℝ→[0,1] is a non-decreasing and right continuous step function such that g(x)=0 for all x≤0 and g(x)=1 for all x≥1. Let us define g⁻¹ as follows…
Q21Consider an exchange economy with two agents, 1 and 2, and two goods, X and Y. There are 6 units of X and 4 units of Y available. Agent 1 has the…
Q23The market for widgets has demand Q=100-10p, where Q is quantity demanded and p is the price in rupees. There are 10 price-taking firms, each with…
Q24A consumer has utility u(x₁,x₂)=min {3x₁+x₂, x₁+2x₂}. Prices are p₁ and p₂. The consumer buys positive quantities of both goods if and only if the…
Q25A consumer's utility over three goods X,Y,Z is U=y min {x,z}. All three prices are equal. Three deals are offered: Deal I: get a unit of Z free with…
Q26Two widget producers, A and B, operate in perfectly competitive input and output markets. Firm A uses capital (k) and labour (l) with f₁(k₁,l₁)=(k₁…
Q27A student may take a test at most three times. Each attempt's score is an independent draw from the uniform distribution on [0,100]. After seeing a…
Q28(Same three-attempt test as the previous question, scores i.i.d. uniform on [0,100] .) Now the university allows the third (final) test only if the…
Q29Consider a homogeneous-goods market with two firms. Let x₁ and x₂ be the quantities of Firms 1 and 2, and X=x₁+x₂. Inverse demand is P=a-bX, with…
Q30Consider a homogeneous-goods market with two firms. Let x₁ and x₂ be the quantities of Firms 1 and 2, and X=x₁+x₂. Inverse demand is P=a-bX, with…
Q31Four cities A, B, C, D sit at the vertices of a square ABCD, connected by roads forming the four sides. If Mr. Rand Walker is at city i in period t…
Q32(Same random walk on the square as the previous question, starting at city A at t=0 .) What is the probability that Mr. Walker never visits city A…
Q33In a railway signalling system a signal is received by station A from the traffic control office and then transmitted to station B. At the origin…
Q34Suppose X has a normal distribution with mean 0 and variance σ². Let Y be an independent random variable taking values -1 and 1 with equal…
Q35According to the Ricardian equivalence proposition, a reduction in the current (lump-sum) taxation of household income:
Q36Tobin's q theory suggests that firms will find it profitable to invest when the value of Tobin's q is:
Q37Consider an agrarian economy with two single-membered households engaged in own cultivation using their family land, labour and capital. Each…
Q38Consider an agrarian economy with two single-membered households engaged in own cultivation using their family land, labour and capital. Each…
Q39Consider an agrarian economy with two single-membered households engaged in own cultivation using their family land, labour and capital. Each…
Q40Consider an agrarian economy with two single-membered households engaged in own cultivation using their family land, labour and capital. Each…