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1. There 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. The number of ways in which this committee can be formed is a) 16 b) 44 c) 32 d) 562. For any sets E & F, E – F = { x ? E | }, x ? F ? and n refer to the Union and intersection of the sets. Consider the following statements for the sets A, B and C i. A - (B ?C) = (A - B) ? (A - C) ii. A - (B ?C) = (A - B) n (A - C) iii. A - (B ?C) = (A - B) n C a) i. is true b) ii. is true c) iii. is true d) none of them is necessarily true.3. ? 8 - 96.1 2/ 2 x e dx is approximately a) 0.025 b) 2 p c) .0 025/ p d) 0.025 2 p4. Consider maximizing 2 2 f (x, y) = x - y subject to the constraint 1 x + y = , where x and y are real numbers. This problem has a) no solution. b) a unique solution. c) 2 solutions. d) an infinity of solutions. 5. Suppose 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. Suppose the equation P(x) = Q(x) has at least (n + 1) distinct solutions. Which of the following choices best describes what this situation implies? a) m = k = n b) m = k 6. There are three alternative definitions of a consistent estimator I. An estimator is consistent if its probability limit equals its true parameter value as sample size approaches infinity. II. An estimator is consistent if its mean squared error goes to zero as sample size approaches infinity. III. An estimator is consistent if it is unbiased, and its variance goes to zero as sample size approaches infinity. Which of the following is correct? a) Only I is Correct b) Only II is Correct c) Only III is Correct d) All three are Correct7. Given the data SXY = 350, SX = 50, SY = 60, N = 10, V(X) = 4, V(Y) = 9, where V(.) refers to the population variance. The correlation coefficient between X and Y, the regression (slope) coefficient of Y on X, and the regression (slope) coefficient of X on Y are, respectively: a) 35/36, 35/16, 35/81 b) 5/6, 5/4, 5/9 c) 5/6, 35/16, 35/81 d) 35 , 35/16, 35/81 36/818. In a surprise check in a local bus, 20 passengers were caught without tickets. The sum of squares and the population standard deviation of the amount in their pockets were Rs. 2000 and Rs. 6, respectively. If the total fine equals the total amount discovered on them, and a uniform fine is imposed, then the fine imposed on an individual is: a) Rs. 8 b) Rs. 6 c) Rs. 10 d) Rs. 129. In a linear regression of Y on X, changing the units of measurement of the Y variable will affect all of the following except: a) the estimated intercept parameter b) the estimated slope parameter c) the Total Sum of Squares for the regression d) R squared for the regression10. A fair dice 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 number that shows up and Y the money I win. [Note: Y < 0 if I lose money.] Which of the following is incorrect? a) Prob (X > Y) = 1 b) Prob(X= 3 | Y = 1) = 1/3 c) E(Y) = 0 d) Prob(Y = 1| X =5) = 1 11. Your 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 x and 2 units of y. If you spent all your income on x, how many units of x could you buy? a) 7 b) 16 c) 15 d) 1812. The demand function for lemonade is Q p d =100 , and the supply function is - Q p s =10 + 2 , where p is the price in rupees. The government levies a sales tax on lemonade after which the volume of sales drops to 60. Then the per unit tax on lemonade is a) Rs 20 b) Rs 15 c) Rs. 10 d) Rs. 513. There are only two price taking firms in a market. Their cost functions are 2 1 1 C = x and 2 2 2 C = 2x , where xi is the output of the ith firm. Market supply is sum of the two firms output. Then the market supply function is a) 4 3p x = b) 3 4 p x = c) 2 p x = d) x = 2 p14. A 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 profit maximizing output equals: a) 3/2 b) 2 c) 5/2 d) Both 3/2 and 5/215. A firm has the production function y = min{L+2K, 2L + K}, where y is quantity of output, and L & K are the quantities of labour and Capital inputs respectively. If the input price of L is Rupee 1 and the input price of K is Rupees 2, then to produce y = 12 costs the firm at least a) 10 Rupees b) 12 Rupees c) 14 Rupees d) 16 Rupees16. The opportunity cost of holding money (that yields zero nominal return) vis-à-vis some interest bearing bond is: a) the real interest rate b) the nominal interest rate c) the real interest rate when measured in real terms and the nominal interest rate when measured in nominal terms d) None of the above17. In the IS-LM framework, an increase in the expected rate of inflation results in a) an increase in the equilibrium value of income and an increase in the equilibrium value of real interest rate b) a decrease in the equilibrium value of income and a decrease in the equilibrium value of real interest rate c) an increases in the equilibrium value of income and a decrease in the equilibrium value of real interest rate d) a decrease in the equilibrium value of income and an increase in the equilibrium value of real interest rate18. When the nominal wage rate is rigid, the aggregate supply schedule (in the output-price space) is: a) horizontal b) vertical c) downward sloping d) upward sloping19. In the IS-LM framework with an external sector i.e., the IS equation now includes a net export term, an appreciation of the (real) exchange rate a) would necessarily result in a decrease in the equilibrium value of income b) would result in a decrease in the equilibrium value of income only if the LM curve is vertical c) would result in a decrease in the equilibrium value of income only if the Marshall-Lerner condition is satisfied d) would result in a decrease in the equilibrium value of income only if the government maintains a balanced budget20. According to the Baumol-Tobin Model, if income rises by ten percent, the transactions demand for money should rise by a) Five percent b) Ten Percent c) Between five and ten percent d) None of the above
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