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Delhi University Entrance Test (DUET) 2020 Previous Year Question Paper With Answer Key

DU MPhil Phd in Economics
Topic: ECO MPHIL S2
1) A student is answering a multiplechoice examination. Suppose a question has m possible answers. The student
knows the correct answer with probability p. If the student knows the correct answer, she picks it with probability 1;
otherwise, she picks randomly from the choices with probability 1/m each. Given that the student picked the correct
answer, the probability that she knew the correct answer is
[Question ID = 5996]
1. mp/[1 + (m - 1)p] [Option ID = 23978]
2. mp/[1 + (1 - p)m] [Option ID = 23979]
3. p/[1 + (m - 1)p] [Option ID = 23980]
4. p/[1 + (1 - p)m] [Option ID = 23981]
Correct Answer :
mp/[1 + (m - 1)p] [Option ID = 23978]
2) A doctor testing a diagnostic tool for a rare disease wants to minimise the chance that the test will find a patient to be
healthy when she is in fact sick (the null hypothesis being that the patient is healthy). The doctor should minimise the
probability of
[Question ID = 5997]
1. Type I error, which would denote a false positive [Option ID = 23982]
2. Type II error, which would denote a false positive [Option ID = 23983]
3. Type I error, which would denote a false negative [Option ID = 23984]
4. Type II error, which would denote a false negative [Option ID = 23985]
Correct Answer :
Type I error, which would denote a false negative [Option ID = 23984]
3) A and B play a bestofseven tabletennis match, i.e., the first to win four games will win the match. The two players
are equally likely to win any of the games in the match. The probability that the match will end in 6 games is
[Question ID = 5998]
1. less than the probability that it will end in 7 games
[Option ID = 23986]
2. equal to the probability that it will end in 7 games
[Option ID = 23987]
3. greater than the probability that it will end in 7 games
[Option ID = 23988]
4. None of these
[Option ID = 23989]
Correct Answer :
equal to the probability that it will end in 7 games
[Option ID = 23987]
4) What is the probability that at least one 6 appears when 6 fair dice are rolled?
[Question ID = 5999]
1. (5/6)
6 [Option ID = 23990]
2. 1/6 [Option ID = 23991]
3. 1 - (5/6)
6 [Option ID = 23992]
4. 5/6 [Option ID = 23993]
Correct Answer :
1 - (5/6)
6 [Option ID = 23992]
5) A family has two children. Each child is a girl with probability 1/2. If at least one child is a girl, then the probability
that both children are girls is
[Question ID = 6000]
1. 1/2 [Option ID = 23994]
2. 1/3 [Option ID = 23995]
3. 3/4 [Option ID = 23996]
4. 2/3 [Option ID = 23997]
Correct Answer :
1/3 [Option ID = 23995]

---

6) In a roll of two fair dice, X is the number on the first die and Y is the number on the second die. Which of the following
statements is true?
[Question ID = 6001]
1. X and Y are independent random variables
2
[Option ID = 23998]
2. X - Y and X + Y are dependent random variables
[Option ID = 23999]
3. X and Y
2
are independent random variables
2
[Option ID = 24000]
4. All of these
[Option ID = 24001]
Correct Answer :
All of these
[Option ID = 24001]
7) You have a single draw from a Bernoulli distribution. The maximum likelihood estimate of the probability of success p is
[Question ID = 6002]
1. 0 [Option ID = 24002]
2. 1 [Option ID = 24003]
3. either 0 or 1 [Option ID = 24004]
4. strictly between 0 and 1 [Option ID = 24005]
Correct Answer :
either 0 or 1 [Option ID = 24004]
8) If X and Y are independent random variables with uniform distributions on the interval [0, 1], and Z = min{X, Y}, then
Pr[Z < 0.5] equals
[Question ID = 6003]
1. 0.25
[Option ID = 24006]
2. 0.5
[Option ID = 24007]
3. 0.625
[Option ID = 24008]
4. 0.75
[Option ID = 24009]
Correct Answer :
0.75
[Option ID = 24009]
9) A student has the opportunity to take a test at most thrice. The student knows that each time he takes the test, his
score is an independent random draw from the uniform distribution on the interval [0, 100]. After learning his score on a
test, the student can either stop and accept it as his official score, or he can discard the result and retake the test. If the
student rejects his score twice and takes the test a third time, that score will be his official score. If his objective is to
maximise his expected official score, the student will decide to be retested after the very first test if and only if his score
is less than
[Question ID = 6004]
1. 50 [Option ID = 24010]
2. 62.5 [Option ID = 24011]
3. 75 [Option ID = 24012]
4. 87.5 [Option ID = 24013]
Correct Answer :
50 [Option ID = 24010]
10) Suppose four fair coins are tossed simultaneously. Suppose E is the event "the number of Heads strictly exceeds
the number of Tails" and F is the event "the number of Tails strictly exceeds the number of Heads". What is the probability
of the event E F ?
[Question ID = 6005]
1. 5/8 [Option ID = 24014]
2. 1/2 [Option ID = 24015]
3. 3/4 [Option ID = 24016]
4. 3/8 [Option ID = 24017]

---

Correct Answer :
3/8 [Option ID = 24017]
11) Suppose X and Y are independent random variables with standard Normal distributions. The probability of X <-1 is some
p (0,1). What is the probability of the event: X >1 and Y
2
<-1?
3
[Question ID = 6006]
1. 3p
[Option ID = 24018]
2. p2
[Option ID = 24019]
3. 2p2
[Option ID = 24020]
4. 3p2
[Option ID = 24021]
Correct Answer :
2p2
[Option ID = 24020]
12) A coin toss has possible outcomes H and T with probabilities 3/4 and 1/4 respectively. A gambler observes a sequence
of tosses of this coin until H occurs. If the first H occurs on the nth toss, then the gambler's prize is 2n. The expected
value of the gambler's prize is
[Question ID = 6007]
1. 1 [Option ID = 24022]
2. 2 [Option ID = 24023]
3. 3 [Option ID = 24024]
4. 4 [Option ID = 24025]
Correct Answer :
3 [Option ID = 24024]
13) Let w = W/P be the real wage rate, where W is the nominal wage rate and P is the aggregate price level. The demand
function for labour is D(w) = 1 - w and the supply function of labour is S(w) = w. If N is the employment level, then f(N) is
the aggregate output. If the nominal wage adjusts to clear the labour market, then the aggregate supply curve is given by
[Question ID = 6008]
1. Y = P f(N) [Option ID = 24026]
2. Y = f(N) [Option ID = 24027]
3. Y = P f(1/2) [Option ID = 24028]
4. Y = f(1/2) [Option ID = 24029]
Correct Answer :
Y = f(1/2) [Option ID = 24029]
14) Suppose a consumer lives for two periods and chooses consumptions C1 and C2 to maximize utility
Future consumption is discounted by . The intertemporal elasticity of substitution in consumption between the two periods
is
[Question ID = 6009]
1.
[Option ID = 24030]
2.
[Option ID = 24031]
3. 1
[Option ID = 24032]
4.
[Option ID = 24033]
Correct Answer :
[Option ID = 24031]
15) Suppose the economywide union sets wage for employed workers by
with unemployment rate and
labor force of the economy . The producer levies price over wage with markup
as
. If each employed

---

worker produces one unit of output , then the aggregate supply function is
[Question ID = 6010]
1.
[Option ID = 24034]
2.
[Option ID = 24035]
3.
[Option ID = 24036]
4.
[Option ID = 24037]
Correct Answer :
[Option ID = 24034]
16) Which of the following would make the LM curve flatter in the
space?
[Question ID = 6011]
1. An increase in income sensitivity of money demand
[Option ID = 24038]
2. An increase in interest sensitivity of planned investment
[Option ID = 24039]
3. An increase in the marginal propensity to consume
[Option ID = 24040]
4. An increase in the interest sensitivity of money demand
[Option ID = 24041]
Correct Answer :
An increase in the interest sensitivity of money demand
[Option ID = 24041]
17) In the MundellFleming model with fixed exchange rates and perfect capital mobility, an increase in government
spending will lead to
[Question ID = 6012]
1. a deterioration in the trade balance [Option ID = 24042]
2. an improvement in the trade balance [Option ID = 24043]
3. no change in the trade balance [Option ID = 24044]
4. an increase in export without affecting imports [Option ID = 24045]
Correct Answer :
a deterioration in the trade balance [Option ID = 24042]
18) Suppose that the markup over cost is 25% for a representative firm in an economy with labour being the single factor; and the
wagesetting equation is
where, = the unemployment rate, = Price and = wage rate. Then the natural rate of
unemployment is:
[Question ID = 6013]
1. 20%
[Option ID = 24046]
2. 17%
[Option ID = 24047]
3. 13%
[Option ID = 24048]
4. 10%
[Option ID = 24049]
Correct Answer :
20%
[Option ID = 24046]
19) Assume that the aggregate production of an economy is
where
and
i.e., the
notation and meanings correspond to the setting for the Solow Model with constant population. Then, the savings rate that
maximizes the steady state level of per capita consumption equals

---

[Question ID = 6014]
1. /(1 + )
[Option ID = 24050]
2. 1/2
[Option ID = 24051]
3. 1/(1 + )
[Option ID = 24052]
4. None of these
[Option ID = 24053]
Correct Answer :
1/2
[Option ID = 24051]
20) A consumer lives for periods 1 and 2. Her lifetime utility function is
.
She earns
and
in the two periods, and her consumptions and satisfy a lifetime budget constraint
Let
for
If
, then
[Question ID = 6015]
1.
[Option ID = 24054]
2.
[Option ID = 24055]
3.
[Option ID = 24056]
4. None of these
[Option ID = 24057]
Correct Answer :
[Option ID = 24055]
21) Consider the Solow model with a positive savings rate, positive population growth rate, and positive rate of
depreciation. Let be the steady state capitallabour ratio.
Suppose and
are capitallabour ratios such that
. Let and be the growth rates of per capita output at
and
respectively. Then
[Question ID = 6016]
1.
[Option ID = 24058]
2.
[Option ID = 24059]
3.
[Option ID = 24060]
4. None of these
[Option ID = 24061]
Correct Answer :
[Option ID = 24058]
22) Consider a small open economy with perfect capital mobility. If there is a positive productivity shock in the economy,
then
[Question ID = 6017]
1. There will be net capital inflow [Option ID = 24062]
2. There will be net capital outflow [Option ID = 24063]
3. Net capital inflow is zero [Option ID = 24064]
4. Investment demand will fall [Option ID = 24065]

---

Correct Answer :
There will be net capital inflow [Option ID = 24062]
23) Consider the game
where the row player's payoff is given first, followed by the column player's payoff. Which of the following statement is
false?
[Question ID = 6018]
1. Row player has a weakly dominated strategy
[Option ID = 24066]
2. Column player has a strictly dominated strategy
[Option ID = 24067]
3. There is a Nash equilibrium of this game in which both players play weakly dominated strategies
[Option ID = 24068]
4. There is a Nash equilibrium of this game in which the column player plays a strictly dominated strategy
[Option ID = 24069]
Correct Answer :
There is a Nash equilibrium of this game in which the column player plays a strictly dominated strategy
[Option ID = 24069]
24) Consider the game
where the row player's payoff is given first, followed by the column player's payoff. This game has only one Nash equilibrium
when
[Question ID = 6019]
1.
[Option ID = 24070]
2.
[Option ID = 24071]
3.
[Option ID = 24072]
4.
[Option ID = 24073]
Correct Answer :
[Option ID = 24072]
25) Voters arrive at a social ranking of alternatives by consulting a `holy book': the social ranking is the ranking found in
this book. Which of Arrow's axioms defining an attractive preference aggregation method is violated by this method?
[Question ID = 6020]
1. Unrestricted domain [Option ID = 24074]
2. The Pareto principle [Option ID = 24075]
3. Independence of irrelevant alternatives [Option ID = 24076]
4. Nondictatorship [Option ID = 24077]
Correct Answer :
The Pareto principle [Option ID = 24075]
26)
[Question ID = 6021]
1.
[Option ID = 24078]
2.

---

[Option ID = 24079]
3.
[Option ID = 24080]
4.
[Option ID = 24081]
Correct Answer :
[Option ID = 24078]
27) Consider an exchange economy with two agents, 1 and 2, and two goods, and . Each agent's consumption set is
.
Given bundles
,

such that
and
, agent 1 strictly prefers
. (In any commodity
bundle, the first entry is a quantity of and the second one is a quantity of
Consider the following claims: In a competitive equilibrium for this economy,
I. Both prices must be positive, and
II. The sum of the allocations to 1 and 2 must equal the sum of their endowments
Which of the following statements is correct?
[Question ID = 6022]
1. I and II are true
[Option ID = 24082]
2. I and II are false
[Option ID = 24083]
3. I is true, but II is false
[Option ID = 24084]
4. I is false, but II is true
[Option ID = 24085]
Correct Answer :
I and II are true
[Option ID = 24082]
28)
[Question ID = 6023]
1. has a subgame perfect equilibrium in which 2 plays
[Option ID = 24086]
2. has three subgame perfect equilibria
[Option ID = 24087]
3. has a unique Nash equilibrium outcome
[Option ID = 24088]
4. has a unique Nash equilibrium
[Option ID = 24089]
Correct Answer :
has a unique Nash equilibrium outcome
[Option ID = 24088]
29) Duopolist firms 1 and 2 sell a homogeneous good in a market with demand function

, where Q is the
quantity demanded at price P. Firms 1 and 2 have constant marginal costs of 0 and 30 respectively. The firms
simultaneously announce prices and consumers buy from the firm whose price is lower. If the firms choose the same price,
all the consumers buy from firm 1. Firm 1's equilibrium price is
[Question ID = 6024]
1. 0
[Option ID = 24090]
2. 20
[Option ID = 24091]

---

3. 25
[Option ID = 24092]
4. 30
[Option ID = 24093]
Correct Answer :
25
[Option ID = 24092]
30)
[Question ID = 6025]
1.
[Option ID = 24094]
2.
[Option ID = 24095]
3.
[Option ID = 24096]
4.
[Option ID = 24097]
Correct Answer :
[Option ID = 24094]
31) A monopolist with unknown cost function faces the demand function
. Which of the following choices of
output cannot be a profit maximising choice?
[Question ID = 6026]
1. 20
[Option ID = 24098]
2. 30
[Option ID = 24099]
3. 40
[Option ID = 24100]
4. 50
[Option ID = 24101]
Correct Answer :
50
[Option ID = 24101]
32) Persons 1, 2 and 3 have to divide 12 indivisible chocolates among themselves. Each person's preference is strictly increasing in chocolates. The procedure
for dividing the chocolates is as follows. Person 1 proposes a division. Each person votes either
or
. If at least two persons vote , then the proposal
is implemented. If not, then Person 1 is eliminated from the voting and Person 2 makes a proposal. Now, only persons 2 and 3 can vote Y or N. If at least one of
them votes Y, then Person 2's proposal is implemented. Otherwise, Person 3 makes a proposal, which will be implemented.
What division of chocolates will occur from a subgame perfect equilibrium of this game?
(Assume that a person votes if voting and are expected to result in the same number of chocolates for that person.)
[Question ID = 6027]
1. 1 gets 12, 2 gets 0, 3 gets 0
[Option ID = 24102]
2. 1 gets 4, 2 gets 4, 3 gets 4
[Option ID = 24103]
3. 1 gets 11, 2 gets 1, 3 gets 0
[Option ID = 24104]
4. 1 gets 11, 2 gets 0, 3 gets 1
[Option ID = 24105]

---

Correct Answer :
1 gets 11, 2 gets 0, 3 gets 1
[Option ID = 24105]
33) Persons 1, 2 and 3 have to divide 12 indivisible chocolates among themselves. Each person's preference is strictly increasing in chocolates. The procedure
for dividing the chocolates is as follows. Person 1 proposes a division. Each person votes either
or
. If at least two persons vote , then the
proposal is implemented. If not, then Person 1 is eliminated from the voting and Person 2 makes a proposal.
Now, only persons 2 and 3 can vote or . If both the remaining voters, 2 and 3, vote , then Person 2's proposal is
implemented. Otherwise, Person 3 makes a proposal, which will be implemented.
What division of chocolates will occur from a subgame perfect equilibrium of this game?
(Assume that a person votes if voting and are expected to result in the same number of chocolates for that
person.)
[Question ID = 6028]
1. 1 gets 12, 2 gets 0, 3 gets 0
[Option ID = 24106]
2. 1 gets 4, 2 gets 4, 3 gets 4
[Option ID = 24107]
3. 1 gets 11, 2 gets 1, 3 gets 0
[Option ID = 24108]
4. 1 gets 11, 2 gets 0, 3 gets 1
[Option ID = 24109]
Correct Answer :
1 gets 11, 2 gets 1, 3 gets 0
[Option ID = 24108]
34) Consider a country with two citizens, 1 and 2. The government is considering a scheme that will cost 100. The government does not know the true
benefits of the scheme to the citizens, say
and
, and must decide whether to implement the scheme on the basis of their reported benefits, say
and

. It will implement the scheme if and only if
. If it is implemented, the government will impose tax
on person 1 and tax
on person 2. Each citizen's reported benefit seeks to maximize the difference between her true benefit known only to her and the tax that
must be paid if and only if the scheme is implemented. The optimal choices of
and
must be such that
[Question ID = 6029]
1.
[Option ID = 24110]
2.
[Option ID = 24111]
3.
[Option ID = 24112]
4.
[Option ID = 24113]
Correct Answer :
[Option ID = 24111]
35) The market for good has the demand function
. There are ten pricetaking firms, each having a cost function
, where is
the firm's own output. There is no new entry. Prices and costs are in terms of rupees per unit. The equilibrium price in this market is
[Question ID = 6030]
1. Rs. 20
[Option ID = 24114]
2. Rs. 15
[Option ID = 24115]
3. Rs. 10
[Option ID = 24116]
4. Rs. 5
[Option ID = 24117]
Correct Answer :

---

Rs. 5
[Option ID = 24117]
36) A sequence of real numbers
converges to .
Consider the following claims:
(I) The sequence
converges to 1.
(II) The sequence
converges to
[Question ID = 6031]
1. Only Statement I is correct
[Option ID = 24118]
2. Only statement II is correct
[Option ID = 24119]
3. Both the statements are correct
[Option ID = 24120]
4. None of the statements is correct
[Option ID = 24121]
Correct Answer :
Both the statements are correct
[Option ID = 24120]
37) Let be the set of real numbers and let be the set of functions
that satisfy the following properties for
all

if and only if

Which of the following is not a function in ?
[Question ID = 6032]
1.
[Option ID = 24122]
2.
[Option ID = 24123]
3.
[Option ID = 24124]
4.
[Option ID = 24125]
Correct Answer :
[Option ID = 24125]
38) Let be the set of real numbers and let
be a concave function.
Which of the following statements is correct?
[Question ID = 6033]
1.
must be concave
[Option ID = 24126]
2.
must be concave
[Option ID = 24127]
3.
(the composition of f with itself) must be concave
[Option ID = 24128]
4.
must be concave

---

[Option ID = 24129]
Correct Answer :
must be concave
[Option ID = 24129]
39)
[Question ID = 6034]
1. 0.25
[Option ID = 24130]
2. 0.5
[Option ID = 24131]
3. 1
[Option ID = 24132]
4. 2
[Option ID = 24133]
Correct Answer :
0.5
[Option ID = 24131]
40) What is the largest set of real numbers on which the function
is negative?
[Question ID = 6035]
1. (1, 3)
[Option ID = 24134]
2. (0, 3)
[Option ID = 24135]
3. (
[Option ID = 24136]
4. (
[Option ID = 24137]
Correct Answer :
(
[Option ID = 24137]
41) Consider the function
[Question ID = 6036]
1. is differentiable at
and its partial derivatives are both 0 at
[Option ID = 24138]
2. is not differentiable at
and its partial derivatives are both 0 at
[Option ID = 24139]
3. is differentiable at
and its partial derivatives are not both 0 at
[Option ID = 24140]
4. is not differentiable at
and its partial derivatives do not exist at
[Option ID = 24141]
Correct Answer :
is not differentiable at
and its partial derivatives are both 0 at
[Option ID = 24139]
42) The coefficient of in
is
[Question ID = 6037]
1. 36
[Option ID = 24142]
2. 66
[Option ID = 24143]
3. 16

---

[Option ID = 24144]
4. 86
[Option ID = 24145]
Correct Answer :
66
[Option ID = 24143]
43) Consider the set
[Question ID = 6038]
1. A is open in
[Option ID = 24146]
2. A is closed in
[Option ID = 24147]
3. A is open and closed in
[Option ID = 24148]
4. A is neither open, nor closed in
[Option ID = 24149]
Correct Answer :
A is neither open, nor closed in
[Option ID = 24149]
44) If
is a continuous function and is a closed subset of , then the set
is
[Question ID = 6039]
1. Open
[Option ID = 24150]
2. Closed
[Option ID = 24151]
3. Neither open, nor closed
[Option ID = 24152]
4. Open and closed
[Option ID = 24153]
Correct Answer :
Closed
[Option ID = 24151]
45)
[Question ID = 6040]
1. A local minimum
[Option ID = 24154]
2. A local maximum
[Option ID = 24155]
3. A point of inflection
[Option ID = 24156]
4. None of these
[Option ID = 24157]
Correct Answer :
A point of inflection
[Option ID = 24156]
46)
The range of this function is
[Question ID = 6041]
1. The 45 degree line

---

[Option ID = 24158]
2. A ray through the origin but not the 45 degree line
[Option ID = 24159]
3. The entire plane
[Option ID = 24160]
4. The first and third quadrants
[Option ID = 24161]
Correct Answer :
The entire plane
[Option ID = 24160]
47)
[Question ID = 6042]
1. 1
[Option ID = 24162]
2. 2
[Option ID = 24163]
3.
[Option ID = 24164]
4. Cannot be determined
[Option ID = 24165]
Correct Answer :
2
[Option ID = 24163]
48) Suppose
satisfies
for all
.
Consider the statements:

for every


[Question ID = 6043]
1.
[Option ID = 24166]
2.
[Option ID = 24167]
3. Both are true
[Option ID = 24168]
4. Both are false
[Option ID = 24169]
Correct Answer :
Both are true
[Option ID = 24168]
49) Consider the function
defined by
.
Of the functions
, defined as follows
,
,
, the functions that divide
without a
remainder are
[Question ID = 6044]
1. Only
[Option ID = 24170]
2.
[Option ID = 24171]
3. Only
[Option ID = 24172]
4.

---

[Option ID = 24173]
Correct Answer :
[Option ID = 24171]
50)
[Question ID = 6045]
1.
is negative definite
[Option ID = 24174]
2.
is positive definite
[Option ID = 24175]
3.
is negative semidefinite
[Option ID = 24176]
4.
is positive semidefinite
[Option ID = 24177]
Correct Answer :
is positive semidefinite
[Option ID = 24177]

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