ISI Admission Test 2021 Question Paper MS (QE) PEA

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ISI 2021
Question Paper · MS
(QE) PEA
EXAM YEAR TYPE SUBJECT

ISI 2021 Question Paper MS (QE) PEA

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P∞ 2n +2 2
1. If the nth partial sum of the series n=1 an is sn = 3n 2 +1 , then
P∞
n=1 an is

(A) 0
(B) divergent
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(C) 32
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(D) 32
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2.laUsing data from a sample of size n, the intercept and slope coefficients a
ag from an ordinary least squares regression of y on x, are a and b
respectively. Which of the following is false?

Pn
(A) i=1 (yi − a − bxi )xi = 0

(B) n1 ni=1 yi = a + nb ni=1 xi
P P
Pn 2
(C) a and b are the solution to minα,β i=1 (yi − α − βxi ) = 0
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a and b are the solution to minα,β ni=1 |yi − α − βxi | = 0
P
(D)

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a z = 2x + 3y. For what price ratio , px

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3. Consider a production function
a y, i.e. (x = 0) be possible, if the objective is
py
will a corner solution in
to minimize the cost of producing a given positive quantity z0 of z?
px px
(A) py
= 2/3 (B) py
≥ 2/3
px px
(C) py
< 2/3 (D) py
≤ −2/3

4. A number is chosen randomly from the first billion natural numbers.
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The probability that the product of the number with its two immedi-
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ate successors is divisible by 24 is closest to

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(B) 3
(C) 5
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2 4 8 3

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ag 5. Each of the four entries of a 2 × 2 matrix is filled by independently
choosing either 1 or −1 uniformly at random. What is the probablity
that the matrix is singular?
1 1
(A) 16 (B) 4
1 1
(C) 2
(D) 3

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6. We need to fill a 3 × 3 matrix by either 0 or 1 such that each row
has exactly one 0 and each column has exactly one 0. The number of
ways we can do this is
(A) 8 (B) 6
(C) 4 (D) 2

7. Let f : [0, 1] → R be a convex function with f (0) = 0. Which of the
following is always true for f ?

(A) f is differentiable
(B) f may not be differentiable but it is continuous
(C) f (x) ≥ xf 0 (x) for all x ∈ [0, 1] if f is differentiable
(D) none of the above

8. If f : R → R is strictly quasi-concave, then it follows that

(A) f is not strictly convex
(B) f is not linear
(C) f is monotonic
(D) if f is quadratic, then the coefficient of x2 ≤ 0

9. The rank of the matrix
 
2 1 0
 1 2 −1
 

−1 1 1

is
(A) 0 (B) 1
(C) 2 (D) 3

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10. Let V be the vector space of polynomials p(x) of degree less than or
equal to 2 that have real coefficients. Then T is a linear transforma-
tion from V to V if T is defined by
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m . = x + p(x) s e
(A) T (p(x))
s e T (p(x)) = xp(x) l a
g a
l (C) T (p(x)) =
(B)
ag
a R
dp(x)
dx

(D) T (p(x)) = p(x)dx where the constant of integration is taken to
be zero.

11. X is a random variable that can take values only in [0, 10].
P (X > 5) ≤ 25 and P (X < 1) ≤ 12 . Then
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(A) E(X) ≥ 1
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(B) E(X) ≤ 5
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a ≤ 8.5
(C) E(X) ≥ 0.5 and E(X)
(D) None of the above is true

12. Given data (−1, 1), (0, 0), (1, 1) on (x, y), the standard deviations of
x and y and the correlation coefficient of x and y are respectively

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√ √ √

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(A) σx = 2/ 3, σy = 2/3, r=0
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las
las (C) σx = 0, σy = 0, r is undefined
ag
ag (D) None of the above

13. An island nation has two potential vaccine firms: denoted as 1 and
2. Both need to invest in R&D to manufacture vaccines. The cost of
R&D for firms 1 and 2 are f1 and f2 respectively. Once R&D is done,
the cost of per unit manufacturing of vaccine is drawn unformly from

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[0, 1]. The firms know their (fixed) cost of R&D but only know that
the cost of per unit manufacturing is uniformly drawn from [0, 1].

Total demand of vaccine is 1 unit and if firm i ∈ {1, 2} supplies
qi ∈ [0, 1] units and has a per unit cost of ci , it incurs a manufacuring
cost of ci qi (along with fi ).

Suppose both firms invest in R&D but only the lowest per unit cost
firm is chosen to supply the entire one unit of vaccine. What is the
total expected cost of vaccination (expected cost is the fixed cost of
R&D and expected cost of manufacturing)?
(A) f1 + f2 + 12 (B) f1 + f2 + 31
(C) f1 + f2 + 23 (D) f1 + f2 + 43

14. India and China produce only shirts and phones using only 2 factors
of production: either higher skilled labour H or low skilled labour L.
Shirts are high skill labour intensive while phones are low skill labour
intensive. The production function for each good is identical in both
countries. India and China have equal amounts of lower skilled labour,
but India has a greater amount of higher skilled labour. Which good
will India import?

(A) Shirts
(B) Phones
(C) Both Shirts and Phones
(D) Neither Shirts nor Phones

15. Consider a duopoly with market demand p = 10−q. The cost function
of firm 1 is 7q1 , and that of firm 2 is 2q2 , where qi is the quantity
produced by firm i, i = 1, 2. In equilibrium, firm 2 charges a price of:
(A) 7 (B) 6
(C) 10 (D) 0

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16. Virat and Mithali eat rice and drink milk in exactly the same quan-
tities. The price of rice falls. In response, Virat increases the amount
of milk but decreases the amount of rice he consumes. Mithali, on the
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other hand, increases both rice and milk consumption. Both Virat
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and Mithali spend all their income on eating rice or drinking milk.
Forem l as
l as Virat’s behaviour to be consistent with standard, well-behaved
indifference curves, his preferences over rice consumption imply that a
g
ag for him, rice must be a:
(A) Inferior good (B) Giffen good
(C) Luxury good (D) Normal good

17. If the short-run IS-LM equilibrium occurs at a level of income above
the natural rate of output, in the long run output will return to the

o m
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natural rate via

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(A) an increase in the price level
s
la rate
(B) a decrease in the interest
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(C) an increase in theamoney supply
(D) a downward shift of the consumption function

18. If the short-run aggregate supply curve is steep, the Phillips curve will
be:
(A) flat

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(B) steep
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(C) backward-bending

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(D) unrelated to the slope of the short-run aggregate supply curve

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a the UK. If the
ag 19. There are no capital controls between the US and
interest rate is higher in the US than in the UK, then we can conclude
that
(A) The US dollar is expected to appreciate with respect to the pound
(the UK’s currency)
(B) The pound is expected to appreciate with respect to the US dollar

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(C) The interest rate in the US is expected to increase
(D) The interest rate in the US is expected to decrease

20. Suppose there are two countries, B and C, that have no trade and no
financial transactions with any countries except each other. B imports
a total of goods worth 10 million bollars from C, where a bollar is a
unit of B’s currency. B has no exports. Which of the following must
be true?
(A) B has a capital account deficit
(B) C has a current account deficit
(C) C is buying assets from B.
(D) The exchange rate of collars per bollar is bigger than 1, where a
collar is a unit of C’s currency.

21. Inventory investment can be expected to
(A) rise when the real interest rate rises, other things being equal
(B) not depend on the real interest rate, other things being equal
(C) fall when the real interest rate rises, other things being equal
(D) depend only on the change in real GDP

22. A cake of size 1 is to be divided among two individuals 1 and 2.
Let xi be the share of the cake going to individual i, i = 1, 2, where
0 ≤ xi ≤ 1. The utility functions are u1 (x1 , x2 ) = x1 , and u2 (x1 , x2 ) =
x2 + |x1 − x2 |, where |a| is the absolute value of a. The Pareto optimal
cake divisions include:
(A) (1, 0) (B) (1/2, 1/2)
(C) (3/4, 1/4) (D) None of the above

23. Rohit spends all his money on dosas and filter coffee. He stays in
Delhi where each dosa and filter coffee cost the same. He eats 15
dosas and drinks 35 filter coffees in a week. He gets a chance to move
to either Chennai or Bangalore. In Chennai, he can just afford to have

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40 dosas and 10 filter coffees in a week. Like in Delhi, each dosa and
filter coffee cost the same. In Bangalore, he can just afford to have
10 dosas and 20 filter coffees in a week. Here, 2 filter coffees costs the
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same as 1 dosa. Where will Rohit prefer to stay?
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(A) Delhi (B) Chennai
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(C) (D) Indifferent between Delhi

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and Chennai

24. Consider the IS-LM model with the real interest rate, R, on the
vertical axis and output, Y, on the horizontal axis. Now suppose
that the central bank chooses R for the economy, based on its own
assessment, at R = R̄. In this case the LM curve will

(A) not exist
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(B) will be horizontal at R = R̄
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(C) upward sloping like the usual LM curve
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(D) None of the other options

25. Consider a supply-demand diagram for the labor market with an up-
ward sloping labor supply curve (Ls ) and a downward sloping labor
demand curve (Ld ). Let the wage be on the vertical axis, and the
level of employment (L) be on the horizontal axis. Suppose the wage
is rigid above the equilibrium wage at w̄, i.e., it fails to adjust to clear
the labor market. Then a reduction in labor demand leads to
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(A) A larger reduction in employment compared to the case if. wages

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(B) A smaller reduction in employment compared togthe
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a were flexible
(C) The same reduction in employment compared to the case if wages
were flexible
(D) None of the other options.

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