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

DU MA Economics
Topic: ECO MA S2
1) Consider independently and identically distributed random variables X , . . . , X
1
n with values in [0, 2]. Each of
these random variables is uniformly distributed on [0, 2]. If Y = max{X , . . . , X
1
n}, then the mean of Y is
[Question ID = 5844]
1. [n/(n + 1)]
2 [Option ID = 23370]
2. n/2(n + 1) [Option ID = 23371]
3. 2n/(n + 1) [Option ID = 23372]
4. n/(n + 1) [Option ID = 23373]
Correct Answer :
2n/(n + 1) [Option ID = 23372]
2) 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. Let the first H occur on the n toss. If n is odd, then the gambler's prize is -2
th
n, and
if n is even, then the gambler's prize is 2n. What is the expected value of the gambler's prize?
[Question ID = 5845]
1. 1 [Option ID = 23374]
2. 1 [Option ID = 23375]
3. 3 [Option ID = 23376]
4. 3 [Option ID = 23377]
Correct Answer :
1 [Option ID = 23375]
3) Suppose two fair dice are tossed simultaneously. What is the probability that the total number of spots on the upper
faces of the two dice is not divisible by 2, 3, or 5?
[Question ID = 5846]
1. 1/3 [Option ID = 23378]
2. 2/9 [Option ID = 23379]
3. 4/9 [Option ID = 23380]
4. 7/16 [Option ID = 23381]
Correct Answer :
2/9 [Option ID = 23379]
4) 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, then she picks that answer; 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 = 5847]
1. mp/[1 + (m - 1)p] [Option ID = 23382]
2. mp/[1 + (1 - p)m] [Option ID = 23383]
3. (1 - p)/[1 + (m - 1)p] [Option ID = 23384]
4. (1 - p)/[1 + (1 - p)m] [Option ID = 23385]
Correct Answer :
mp/[1 + (m - 1)p] [Option ID = 23382]
5) Suppose Y is a random variable with uniform distribution on [0, 2]. The value of the cumulative distribution function of
the random variable X = eY at x [1, e ] is
2
[Question ID = 5848]
1. 2 ln x
-1
[Option ID = 23386]
2. 4 ln x - 2
-1
-1 [Option ID = 23387]
3. ln x [Option ID = 23388]
4. ln x - 1 [Option ID = 23389]
Correct Answer :
2 ln x
-1
[Option ID = 23386]
6) Consider an economy where the final commodity is produced by a single firm using labour only. The pricesetting firm
charges a 25% markup over its per unit nominal wage cost. The workers demand a real wage rate W/P = (1 - u), where u
is the unemployment rate, P is the price, and W is the nominal wage rate. The natural rate of unemployment in this
economy is
[Question ID = 5849]
1. 20% [Option ID = 23390]
2. 17% [Option ID = 23391]

---

3. 13% [Option ID = 23392]
4. 10% [Option ID = 23393]
Correct Answer :
20% [Option ID = 23390]
7) The aggregate production function of an economy is Y = (K
1/2
t
L
t
)
t
. Capital grows according to K
= (1 - ) K
t+1
+ S
t
,
t
where S = sY
t
, L
t
=
t
, s is the saving rate, is the depreciation rate and is the total population. Then, the steadystate
level of consumption per capita is
[Question ID = 5850]
1. s/
[Option ID = 23394]
2. s /
2
2
[Option ID = 23395]
3. 1/s
[Option ID = 23396]
4. s(1 - s)/
[Option ID = 23397]
Correct Answer :
s(1 - s)/
[Option ID = 23397]
8) Consider a production technology Y = AL, where Y is output, A is productivity, and L is labour input. A firm sets its
price P at a constant markup ? over the effective wage cost per unit of production W/A. The expected real wage rate of
workers is W/Pe = A(1 - u)
, where 0 < < 1 and P
1-
e is the expected price. If the price expected by workers matches
the actual price level, then the effect of a rise in the level of productivity on unemployment is
[Question ID = 5851]
1. positive
[Option ID = 23398]
2. negative
[Option ID = 23399]
3. zero
[Option ID = 23400]
4. ambiguous
[Option ID = 23401]
Correct Answer :
negative
[Option ID = 23399]
9) A household has an endowment of 1 unit of time. The household maximises its utility u = ln c + b ln(1 - l), where c
denotes consumption and l [0, 1] denotes time spent working. It finances its consumption from labour income wl, where
w is the market wage rate per unit of labour time. If the market wage rate goes up, then equilibrium labour supply of the
household
[Question ID = 5852]
1. increases
[Option ID = 23402]
2. decreases
[Option ID = 23403]
3. remains constant
[Option ID = 23404]
4. changes in an ambiguous manner
[Option ID = 23405]
Correct Answer :
remains constant
[Option ID = 23404]
10) Consider the ISLM model with a given price level P. Investment is a decreasing function of the interest rate and
savings is an increasing function of aggregate income. The demand for real money balances M/P is an increasing function of
aggregate income and a decreasing function of the interest rate. The monetary authority chooses nominal money supply M

---

to ensure that the resulting money market equilibrium keeps the interest rate fixed at some target level. In this setup, an
increase in the target interest rate leads to
[Question ID = 5853]
1. a rise in equilibrium output [Option ID = 23406]
2. a fall in equilibrium output [Option ID = 23407]
3. no effect on equilibrium output [Option ID = 23408]
4. an ambiguous effect on equilibrium output [Option ID = 23409]
Correct Answer :
a fall in equilibrium output [Option ID = 23407]
11) Consider the Solow growth model with a given savings ratio, a constant population growth rate, zero rate of capital
depreciation, and no technical progress. Let k be the steadystate capitallabour ratio in this economy. Suppose the
economy is yet to reach the steadystate and has capitallabour ratio k at time t
1
and capitallabour ratio k
1
at
2
time t , such that t
2
< t
1
and k
2
< k
1
< k
2
. Let the associated growth rates of per capita income at time t and t
1
be g
2
and
1
g respectively. Then, by the properties of the Solow model,
2
[Question ID = 5854]
1. g < g
1
2
[Option ID = 23410]
2. g > g
1
2
[Option ID = 23411]
3. g = g
1
2
[Option ID = 23412]
4. the relationship between g and g
1
is ambiguous
2
[Option ID = 23413]
Correct Answer :
g > g
1
2
[Option ID = 23411]
12) A consumer lives for periods 1 and 2. Given consumptions c and c
1
in these periods, her utility is U = ln c
2
+ (1 +
1
) ln c
-1
. She earns incomes w
-1
2
and w
1
in the two periods and her lifetime budget constraint is c
2
+ (1 + r)
1
c = w
2
+ (1 +
1
r) w
-1
, where r is the interest rate on savings. If r > , then
2
[Question ID = 5855]
1. c > c
1
2
[Option ID = 23414]
2. c < c
1
2
[Option ID = 23415]
3. c = c
1
2
[Option ID = 23416]
4. The relationship between c and c
1
is ambiguous
2
[Option ID = 23417]
Correct Answer :
c < c
1
2
[Option ID = 23415]
13) A consumer lives for periods 1 and 2. Her lifetime utility function is U(c , c
1
) =
2
where 0 < < 1 and c is
i
consumption in period i. The elasticity of substitution between consumption in period 1 and consumption in period 2 is
[Question ID = 5856]
1. 1 +
[Option ID = 23418]
2. 1 -
[Option ID = 23419]
3. 1/(1 + )
[Option ID = 23420]
4. 1/(1 - )
[Option ID = 23421]
Correct Answer :
1/(1 - )
[Option ID = 23421]

---

14) 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 = 5857]
1. less than the probability that it will end in 7 games
[Option ID = 23422]
2. equal to the probability that it will end in 7 games
[Option ID = 23423]
3. greater than the probability that it will end in 7 games
[Option ID = 23424]
4. None of these
[Option ID = 23425]
Correct Answer :
equal to the probability that it will end in 7 games
[Option ID = 23423]
15) Let X and Y be jointly normally distributed, i.e.,
If
and
, then
[Question ID = 5858]
1. the OLS regression of Y on X will yield a slope that is less than unity, and that of X on Y will yield a slope greater than unity
[Option ID = 23426]
2. the OLS regression of Y on X will yield a slope that is less than unity, and that of X on Y will yield a slope less than unity
[Option ID = 23427]
3. the OLS regression of Y on X will yield a slope that is greater than unity, and that of X on Y will yield a slope less than unity
[Option ID = 23428]
4. it is not possible to draw conclusions about the magnitude of the slope with the given information
[Option ID = 23429]
Correct Answer :
the OLS regression of Y on X will yield a slope that is less than unity, and that of X on Y will yield a slope less than unity
[Option ID = 23427]
16) Let ? denote the negation of a statement. Consider a set X and a binary relation on X. Relation is said to be
irreflexive if ?x x for every x X. Relation is said to be transitive if, for all x, y, z X, x y and y z implies x z.
If is asymmetric (i.e., for all x, y X, x y implies ?y x) and negatively transitive (i.e., for all x, y, z X, x y
implies x z, or z y, or both), then is
[Question ID = 5859]
1. irreflexive, but not transitive
[Option ID = 23430]
2. transitive, but not irreflexive
[Option ID = 23431]
3. irreflexive and transitive
[Option ID = 23432]
4. neither transitive, nor irreflexive
[Option ID = 23433]
Correct Answer :
irreflexive and transitive
[Option ID = 23432]
17) Let ? denote the negation of a statement. Consider a set X and a binary relation on X. For all x, y X, we say x y
if and only if ?y x. Relation is said to be total if, for all x, y X, ?x y implies y x.
If is asymmetric (i.e., for all x, y X, x y implies ?y x) and negatively transitive (i.e., for all x, y, z X, x y
implies x z, or z y, or both), then
[Question ID = 5860]
1. is not total
[Option ID = 23434]
2. is total

---

[Option ID = 23435]
3. may not be total
[Option ID = 23436]
4. is not total over a nonempty subset of X
[Option ID = 23437]
Correct Answer :
is total
[Option ID = 23435]
18) Let ? denote the negation of a statement. Consider a set X and a binary relation on X. For all x, y X, we say x y
if and only if ?y x. Relation is said to be transitive if, for all x, y, z X, x y and y z implies x z.
If is asymmetric (i.e., for all x, y X, x y implies ?y x) and negatively transitive (i.e., for all x, y, z X, x y
implies x z, or z y, or both), then
[Question ID = 5861]
1. is not transitive over a nonempty subset of X
[Option ID = 23438]
2. is not transitive
[Option ID = 23439]
3. may not be transitive
[Option ID = 23440]
4. is transitive
[Option ID = 23441]
Correct Answer :
is transitive
[Option ID = 23441]
19) Let ? denote the negation of a statement. Consider a set X and a binary relation on X. For all x, y X, we say x y
if and only if ?x y and ?y x. Relation is said to be transitive if, for all x, y, z X, x y and y z implies x z.
If is asymmetric (i.e., for all x, y X, x y implies ?y x) and negatively transitive (i.e., for all x, y, z X, x y
implies x z, or z y, or both), then
[Question ID = 5862]
1. is transitive
[Option ID = 23442]
2. is not transitive
[Option ID = 23443]
3. may not be transitive
[Option ID = 23444]
4. is not transitive over a nonempty subset of X
[Option ID = 23445]
Correct Answer :
is transitive
[Option ID = 23442]
20) Let ? denote the negation of a statement. Consider a set X and a binary relation on X. For all x, y X, we say x y
if and only if ?x y and ?y x. Relation is said to be symmetric if, for all x, y X, x y implies y x.
If is asymmetric (i.e., for all x, y X, x y implies ?y x) and negatively transitive (i.e., for all x, y, z X, x y
implies x z, or z y, or both), then
[Question ID = 5863]
1. is symmetric
[Option ID = 23446]
2. is not symmetric
[Option ID = 23447]
3. may not be symmetric
[Option ID = 23448]
4. is not symmetric over a nonempty subset of X
[Option ID = 23449]

---

Correct Answer :
is symmetric
[Option ID = 23446]
21) Consider the following game for players 1 and 2. Player 1 moves first and chooses L or R. If she chooses L, then the
game ends and the payoffs are (1, 0), where the first entry is 1's payoff and the second entry is 2's payoff. If she chooses
R, then 2 chooses U or D. If she chooses U, then the game ends and the payoffs are (0, 2). If she chooses D, then 1
chooses L or R. If she chooses L, then the game ends and the payoffs are (4, 0). If she chooses R, then the game ends and
the payoffs are (3, 3). This game has
[Question ID = 5864]
1. one Nash equilibrium in pure strategies [Option ID = 23450]
2. two Nash equilibria in pure strategies [Option ID = 23451]
3. three Nash equilibria in pure strategies [Option ID = 23452]
4. no Nash equilibria in pure strategies [Option ID = 23453]
Correct Answer :
two Nash equilibria in pure strategies [Option ID = 23451]
22) Consider the following game for players 1 and 2. Player 1 moves first and chooses L or R. If she chooses L, then the
game ends and the payoffs are (1, 0), where the first entry is 1's payoff and the second entry is 2's payoff. If she chooses
R, then 2 chooses U or D. If she chooses U, then the game ends and the payoffs are (0, 2). If she chooses D, then 1
chooses L or R. If she chooses L, then the game ends and the payoffs are (4, 0). If she chooses R, then the game ends and
the payoffs are (3, 3). This game has
[Question ID = 5865]
1. one subgame perfect Nash equilibrium [Option ID = 23454]
2. two subgame perfect Nash equilibria [Option ID = 23455]
3. three subgame perfect Nash equilibria [Option ID = 23456]
4. no subgame perfect Nash equilibria [Option ID = 23457]
Correct Answer :
one subgame perfect Nash equilibrium [Option ID = 23454]
23) In a noncooperative game, if a profile of strategies
[Question ID = 5866]
1. is a Nash equilibrium, then it is an equilibrium in dominant strategies [Option ID = 23458]
2. is a Nash equilibrium, then it is a subgame perfect equilibrium [Option ID = 23459]
3. is a Nash equilibrium, then it is a sequential equilibrium [Option ID = 23460]
4. is an equilibrium in dominant strategies, then it is a Nash equilibrium [Option ID = 23461]
Correct Answer :
is an equilibrium in dominant strategies, then it is a Nash equilibrium [Option ID = 23461]
24) If player 1 is the row player and player 2 is the column player in games
then
[Question ID = 5867]
1. 2's payoff in a Nash equilibrium of G cannot be less than 2's payoff in a Nash equilibrium of G
[Option ID = 23462]
2. 2's payoff in a Nash equilibrium of G cannot be less than 2's payoff in a Nash equilibrium of G
[Option ID = 23463]
3. 2's payoff in a Nash equilibrium of G must be equal to 2's payoff in a Nash equilibrium of G
[Option ID = 23464]
4. 2's payoff in a Nash equilibrium of G may be higher than 2's payoff in a Nash equilibrium of G
[Option ID = 23465]
Correct Answer :
2's payoff in a Nash equilibrium of G may be higher than 2's payoff in a Nash equilibrium of G
[Option ID = 23465]
25) Consider an exchange economy with agents 1 and 2 and goods x and y. Agent 1 lexicographically prefers x to y, i.e.,
between two nonidentical bundles of x and y, she strictly prefers the bundle with more of x, but if the bundles have the
same amount of x, then she strictly prefers the bundle with more of y.
Agent 2's utility function is
Agent 1's endowment is
and Agent 2's endowment is
The set of competitive equilibrium price ratios
for this economy is

---

[Question ID = 5868]
1. {1}
[Option ID = 23466]
2. [0,1]
[Option ID = 23467]
3. (0,1]
[Option ID = 23468]
4.
[Option ID = 23469]
Correct Answer :
{1}
[Option ID = 23466]
26) Consider an exchange economy with agents 1 and 2 and goods x and y.
Agent 1 lexicographically prefers y to x, i.e., between two nonidentical bundles of x and y, she strictly prefers the bundle
with more of y, but if the bundles have the same amount of y, then she strictly prefers the bundle with more of x.
Agent 2's utility function is
Agent 1's endowment is
and Agent 2's endowment is
The set of competitive equilibrium price ratios
for this economy is
[Question ID = 5869]
1. {1}
[Option ID = 23470]
2. [0,1]
[Option ID = 23471]
3. (0,1]
[Option ID = 23472]
4.
[Option ID = 23473]
Correct Answer :
(0,1]
[Option ID = 23472]
27) Consider an exchange economy with goods x and y, and agents 1 and 2, whose endowments are
and
respectively.
The utility functions of 1 and 2 are
and
respectively.
The competitive equilibrium price ratio
is
[Question ID = 5870]
1. 9/10
[Option ID = 23474]
2. 10/9
[Option ID = 23475]
3. 1
[Option ID = 23476]
4. 0
[Option ID = 23477]
Correct Answer :
0
[Option ID = 23477]
28) Consider an exchange economy with goods x and y, and agents 1 and 2, whose endowments are
and
respectively.
The utility functions of 1 and 2 are
and
respectively.
The competitive equilibrium allocations are
[Question ID = 5871]

---

1. 1 gets (10 - x, 9 - y) and 2 gets (x, y), where x [9, 10] and y = 9
[Option ID = 23478]
2. 1 gets (x, y) and 2 gets (10 - x, 9 - y), where x [9, 10] and y = 9
[Option ID = 23479]
3. 1 gets (x, y) and 2 gets (9 - x, 10 - y), where x [8, 9] and y = 10
[Option ID = 23480]
4. 1 gets (x, y) and 2 gets (9 - x, 10 - y), where x = 9 and y [9, 10]
[Option ID = 23481]
Correct Answer :
1 gets (x, y) and 2 gets (10 - x, 9 - y), where x [9, 10] and y = 9
[Option ID = 23479]
29) Consider an exchange economy with goods x and y, and agents 1 and 2, whose endowments are
and
respectively.
The utility functions of 1 and 2 are
and
respectively.
The allocation that gives (10, 9) to 1 and (0,0) to 2 is
[Question ID = 5872]
1. Pareto efficient but not a competitive equilibrium allocation
[Option ID = 23482]
2. neither Pareto efficient nor a competitive equilibrium allocation
[Option ID = 23483]
3. a competitive equilibrium allocation that is Pareto efficient
[Option ID = 23484]
4. a competitive equilibrium allocation that is not Pareto efficient
[Option ID = 23485]
Correct Answer :
a competitive equilibrium allocation that is Pareto efficient
[Option ID = 23484]
30) Given a nonempty set C
, for every p
, let c(p) C be such that
for every c C. Then, the
function
given by
is
[Question ID = 5873]
1. linear
[Option ID = 23486]
2. convex
[Option ID = 23487]
3. concave
[Option ID = 23488]
4. quasiconvex
[Option ID = 23489]
Correct Answer :
concave
[Option ID = 23488]
31) Given a nonempty set C
, for every p
, let c(p) C be such that
for every c C. Then, the
function
given by
is
[Question ID = 5874]
1. homogenous of degree 0
[Option ID = 23490]
2. homogenous of degree 1
[Option ID = 23491]
3. homogenous of degree
[Option ID = 23492]
4. nonhomogenous
[Option ID = 23493]
Correct Answer :

---

homogenous of degree 1
[Option ID = 23491]
32) Suppose
is strictly increasing and has the supremum (i.e., least upper bound) . Then, the function
is
[Question ID = 5875]
1. not well defined for some
[Option ID = 23494]
2. bounded above
[Option ID = 23495]
3. unbounded above
[Option ID = 23496]
4. not strictly increasing
[Option ID = 23497]
Correct Answer :
unbounded above
[Option ID = 23496]
33) The interval [0, ) can be expressed as
[Question ID = 5876]
1.
where each
is a rational number
[Option ID = 23498]
2.
where each
and
is a real number
[Option ID = 23499]
3.
where each
and
is an irrational number
[Option ID = 23500]
4. All of these
[Option ID = 23501]
Correct Answer :
where each
is a rational number
[Option ID = 23498]
34) If
is given by
then
[Question ID = 5877]
1. f is differentiable at (0, 0) and both partial derivatives at (0, 0) are 0
[Option ID = 23502]
2. f is nondifferentiable at (0, 0) and both partial derivatives at (0, 0) are 0
[Option ID = 23503]
3. f is differentiable at (0, 0) and neither partial derivative at (0, 0) is 0
[Option ID = 23504]
4. f is nondifferentiable at (0, 0) and neither partial derivative at (0, 0) exists
[Option ID = 23505]
Correct Answer :
f is nondifferentiable at (0, 0) and both partial derivatives at (0, 0) are 0
[Option ID = 23503]
35) Suppose
is a twicedifferentiable function that solves the differential equation
over and
satisfies the condition
for some
. Then,
[Question ID = 5878]
1. f has positive and negative values over (0, k)
[Option ID = 23506]
2. f has only positive values over (0, k)

---

[Option ID = 23507]
3. f has only negative values over (0, k)
[Option ID = 23508]
4. f = -1 on (0, k)
[Option ID = 23509]
Correct Answer :
f has only negative values over (0, k)
[Option ID = 23508]
36) Let be the collection of sets
satisfying: for every
, there are real numbers and such that
and
Let be the collection of sets
satisfying: for every
, there are rational numbers and such that
and
then,
[Question ID = 5879]
1.
[Option ID = 23510]
2.
[Option ID = 23511]
3.
[Option ID = 23512]
4.
[Option ID = 23513]
Correct Answer :
[Option ID = 23512]
37) The set
and
is
[Question ID = 5880]
1. a linear subspace of
[Option ID = 23514]
2. convex
[Option ID = 23515]
3. nonconvex
[Option ID = 23516]
4. a convex polytope
[Option ID = 23517]
Correct Answer :
convex
[Option ID = 23515]
38) Suppose the distance between
is given by
and
is a continuous function. If E is an open subset of
, then
is
[Question ID = 5881]
1. An open subset of
[Option ID = 23518]
2. A closed subset of
[Option ID = 23519]
3. Neither an open, nor a closed, subset of
[Option ID = 23520]
4. An open and closed subset of
[Option ID = 23521]
Correct Answer :
An open subset of

---

[Option ID = 23518]
39) Which of the following two numbers is larger for
?
[Question ID = 5882]
1.
[Option ID = 23522]
2.
[Option ID = 23523]
3. They are equal
[Option ID = 23524]
4. It depends on the value of k
[Option ID = 23525]
Correct Answer :
It depends on the value of k
[Option ID = 23525]
40) Consider the matrix
where
. The inner product of vectors
and
in
is defined by
. So, for
the vectors and in
[Question ID = 5883]
1.
[Option ID = 23526]
2.
[Option ID = 23527]
3.
[Option ID = 23528]
4.
[Option ID = 23529]
Correct Answer :
[Option ID = 23526]
41) Let
be the greatest integer that is less than or equal to
. The function
, defined by
for
,
is
[Question ID = 5884]
1. Leftdiscontinuous at an integer
[Option ID = 23530]
2. Rightdiscontinuous at an integer
[Option ID = 23531]
3. Left discontinuous and rightdiscontinuous at an integer
[Option ID = 23532]
4. Discontinuous everywhere
[Option ID = 23533]
Correct Answer :
Leftdiscontinuous at an integer
[Option ID = 23530]
42)
[Question ID = 5885]
1. Leftdiscontinuous at an integer
[Option ID = 23534]
2. Rightdiscontinuous at an integer
[Option ID = 23535]
3. Left discontinuous and rightdiscontinuous at an integer

---

[Option ID = 23536]
4. Discontinuous everywhere
[Option ID = 23537]
Correct Answer :
Rightdiscontinuous at an integer
[Option ID = 23535]
43) Let
be the greatest integer that is less than or equal to
. Let
be the smallest integer that is greater than or
equal to
. The function
, defined by
for
, is
[Question ID = 5886]
1. Leftdiscontinuous at an integer
[Option ID = 23538]
2. Rightdiscontinuous at an integer
[Option ID = 23539]
3. Left discontinuous and rightdiscontinuous at an integer
[Option ID = 23540]
4. Discontinuous everywhere
[Option ID = 23541]
Correct Answer :
Left discontinuous and rightdiscontinuous at an integer
[Option ID = 23540]
44) If
and
Then,
[Question ID = 5887]
1.
is a subset of C
[Option ID = 23542]
2.
is a subset of C
[Option ID = 23543]
3.
is a subset of C
[Option ID = 23544]
4.
is a subset of C
[Option ID = 23545]
Correct Answer :
is a subset of C
[Option ID = 23543]
45) Consider a 4 x 4matrix A. Obtain matrix B from matrix A by performing the following operations in sequence:
(1) Interchange the first and fourth columns, and then
(2) Interchange the second and fourth rows. Then,
[Question ID = 5888]
1. det A = det B
[Option ID = 23546]
2. det A det B
[Option ID = 23547]
3. det B 0
[Option ID = 23548]
4. det B > 0
[Option ID = 23549]

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Correct Answer :
det A = det B
[Option ID = 23546]
46)
[Question ID = 5889]
1. 1/4
[Option ID = 23550]
2. 1/2
[Option ID = 23551]
3. 4
[Option ID = 23552]
4. 2
[Option ID = 23553]
Correct Answer :
1/4
[Option ID = 23550]
47) Consider a decreasing differentiable function
and an increasing continuous function
. If
satisfies
for every
, then F is
[Question ID = 5890]
1. Increasing over [0, a] and decreasing over [a, ), for some a > 0
[Option ID = 23554]
2. Decreasing over [0, a] and increasing over [a, ), for some a > 0
[Option ID = 23555]
3. Increasing
[Option ID = 23556]
4. Decreasing
[Option ID = 23557]
Correct Answer :
Decreasing
[Option ID = 23557]
48) If
and
are defined by
and
Then
, given by
, is
[Question ID = 5891]
1. Injective but not surjective
[Option ID = 23558]
2. Surjective but not injective
[Option ID = 23559]
3. Neither injective nor surjective
[Option ID = 23560]
4. Bijective
[Option ID = 23561]
Correct Answer :
Bijective
[Option ID = 23561]
49) Given nonempty subsets of
, say
, let
Fix p
. For a nonempty set X
, let

Suppose there exists
such that
, and for every
there exists
such that
.

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Then,

[Question ID = 5892]
1.
[Option ID = 23562]
2.
[Option ID = 23563]
3.
[Option ID = 23564]
4.
[Option ID = 23565]
Correct Answer :
[Option ID = 23563]
50)
If
and
is the transpose of , then
is
[Question ID = 5893]
1. 16
[Option ID = 23566]
2. 16
[Option ID = 23567]
3. 4
[Option ID = 23568]
4. 4
[Option ID = 23569]
Correct Answer :
16
[Option ID = 23566]

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