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Part - 1

1. (c) (20, 0)

2. (b) a vertical line

3. (b) K = (3/2)L

4. (c) MR < 0 in such a case

5. (a) A, B

6. (b) inflation is constant

7. (d) change the composition of monetary base

8. (a) always reduce borrowing

9. (a) improve it in the short run

10. (a) only raises the price level and the interest rate

11. (a) f(x) = x2

12. (c) det A = det B

13. (b) Df(x) = 0 for some x 7 R

14. (d) In every legislature and every party, there exists a legislator who

does not pay taxes

15. (c) singular

16. (b) 2/5

17. (c) increases steadily from 0 to 1

18. (d) 4/7

19. (b) (i) 0.16; (ii) 0.29

20. (c) 7.5

Part - 2

21. (c) 1200-488L+72L2-4L3

22. (d) (i) Rs. 4,80,000 and (ii) risk-averse

23. (a) (i) 1 km and (ii) Rs. 100

24. (a) Some firms will exit the industry, but the others will remain

Entrance Exam solutions economicsentrance.weebly.com beaneconomist.com

25. (b) 9 apples

26. (a) 3.5 kg

27. (d) ((0, 0),(<8, 2),(3-<8, 1))

28. (c) Pareto efficient, because there is a bound on Agent 1â€™s ability to

consume.

29. (b) <2

30. (c) ((0, 0), (0, 3-<3), (3, <3))

31. >/[@(1+>)]

32. (b) P/Pe = 1+>

33. (a) an increase in the actual price level

34. (b) a decrease in the actual price level

35. (a) B2/[1-(@1+B1)] units

36. (c) 1/[1-(@1+B1)+(C1B2)/C2]

37. (c) (1+D)w2 > (1+r)w1

38. (a) goes up

39. (d) Country 1 has a lower equilibrium level of output than country 2

and it runs a trade surplus vis-Ã*-vis Country 2.

40. (b) (i) and (ii) remain unchanged; (iii) depreciates

41. (a) {(x, r) | f(x) K r} is convex

42. (a) 2xesqr(x)-ex

43. (d) converges to neither 1 nor -1

44. (d) [-1, 1]

45. (c) (-1, 1)

46. (d) d(x, z) K d(x, y) +d(y, z)

47. (b) (A-B) X C = (A X C)-(B X C)

48. (c) Attains a saddle point

49. (c) 4.5

50. (d) During warm weather, my crops suffer from pests more than during

cooler weather. Therefore, a warm environment must help pests to

multiply.

51. (d) None of the above

52. (3!3!)/6!

Entrance Exam solutions economicsentrance.weebly.com beaneconomist.com

53. (b) 5/18

54. (b) (Â½, Â¾, Â½)

55. (b) 37.6 years

56. (a) 0.025

57. (d) 5, 0.5, 39

58. (d) 0.79

59. (b) There is a significant difference in the performance of the classes at

the 5% level but no significant difference at the 1% level of significance

60. (b) There is no significant difference between the districts and the

candidate is preferred in district A

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) 56

2. For any sets E & F, E â€“ F = { F x E x | }, and refer to the Union and

intersection of the sets. Consider the following statements for the sets A, B and C

i. C A B A C B A

ii. C A B A C B A

iii. C B A C B A

a) i. is true

b) ii. is true

c) iii. is true

d) none of them is necessarily true.

3. ∫

96 . 1

2 / 2 x e dx is approximately

a) 0.025

b) 2

c) / 025 . 0

d) 0.025 2

4. Consider maximizing 2 2 ) , ( y x y x f subject to the constraint 1 y x , 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 < n

c) P(x) and Q(x) are identical.

d) P(x) and Q(x) are linear

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 Correct

7. Given the data ΣXY = 350, ΣX = 50, ΣY = 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) 36 / 35 , 35/16, 35/81

8. 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. 12

9. 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 regression

10. 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) 18

12. The demand function for lemonade is p Qd 100 , and the supply function is

p Qs 2 10 , 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. 5

13. There are only two price taking firms in a market. Their cost functions are 2

1 1 x C

and 2

2 2 2x C , 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) p x 2

14. A monopoly faces the demand curve P = 8 â€“ 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 5/2

15. 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 Rupees

16. The opportunity cost of holding money (that yields zero nominal return) vis-Ã*-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 above

17. 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 rate

18. 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 sloping

19. 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 budget

20. 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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