# Set Relations & Functions MCQs Part I

1) If
a) d = bc
b) c = bd
c) b = cd
d) none of these

2) The solution of < 1 is
a) -4 < x < -2
b) -4 < x < 2
c) -2 < x < 4
d) 2 < x < 4

3) If x and y be reals, then
holds iff

a) x > Y
b) x < y
c) x = y
d)

4) The solution set of the equation
is

a)
b) {1}
c)
d)

5) The solution of the inequation
is

a)
b)
c)
d)

6) If and
, then
p lies in the interval

a)
b)
c)
d)

7) If
then

a)
b)
c)
d) x < 0

8) If then
a) x < -3
b)
c)
d) none of these

9) If such that is
prime, then the correct relationship is

a)
b)
c)
d)

10) If , then x lies in
the interval

a)
b)
c)
d)

11) Let
be a one – one function and only one of the conditions
is true then the function f is given by the set

a) {(x, a), (y, b), (z, c)}
b) {(x, a), (y, c), (z, b)}
c) {(x, b), (y, a), (z, c)}
d) {(x, c), (y, b), (z, a)}

12) Let S be the set of all functions from the set A to the set A. If n(A)=k
then n(S) is

a) k !
b)
c)
d) none of these

13) Let A = The
total number of distinct relations that can be defined
over
A is

a)
b) 6
c) 8
d) none of these

14) A Survey shows that 63% of the Americans like cheese whereas 76%like apples. If x% of the Americans like both cheese and apples then
a) x=39
b) x=63
c)
d) none of these

15) If ,
and N
is the Universal set ,then is

a) A
b) N
c) B
d) None of these

16) In a town of 10,000 families it was found that 40% families buy newspaper
A, 20% families buy newspaper B and 10% families buy newspaper C,5% families
buy A and B, 3% buy B and C and 4% buy A and C. If 2% families buy all
the three Newspapers, then the number of families which buy A only is

a) 3100
b) 3300
c) 2900
d) 1400

17) Consider the set A of all determinants of order 3 with entries 0 or
1 only. Let B be the subset of A consisting of all determinants with value
1. Let C be the subset of the set of all determinants with value –1.Then

a) C is empty
b) B has many elements as C
c)
d) B has twice as many elements as C

18) If A and B are two sets, then equals
a) A
b) B
c)
d) none of these

19) Let A and B have 3 and 6 elements respectively. What can

be the minimum number of elements in

a) 3
b) 6
c) 9
d) 18

20) If X and Y are two sets, then
equals

a) x
b) Y
c)
d) none of these

21) Let and

Then
is given by

a)
b) x
c)
d) none of these

22) If and ,
then is

a)
b)
c)
d)

23) If
and ,
then
is

a)
b)
c)
d)

24) Let A and B be two sets that
Then is
equal to

a)
b) B
c) A
d) none of these

25) Let A and B be two sets then is
equal to

a)
b) A
c)
d) none of these

26) Let U be the universal set and .
Then is
equal to

a)
b)
c)
d)

27) If A and B are two sets then
is equal to

a)
b)
c) A
d)

28) 20 teachers of a school either teach mathematics or physics. 12 of them
teach mathematics while 4 teach both the subjects. Then the number of teachers
teaching physics only is

a) 12
b) 8
c) 16
d) none of these

29) Of the members of three athletic teams in a school 21are in the cricket
team, 26 are in the hockey team and 29 are in the football team. Among them,
14 play hockey and cricket, 15 play hockey and football, and 12 play football
and cricket. Eight play all the three games. The total number of members in
the three athletic teams is

a) 43
b) 76
c) 49
d) none of these

30) The relation congruence modulo “m” is
a) reflexive only
b) transitive only
c) symmetric only
d) an equivalence relation

31) If
a)
b)
c)
d)

32) If a set A has n elements, then the total number of subsets
of A is

a) 2n
b)
c)
d)

33) If A,B,C be three sets such that
and ,
then

a) A = B
b) B = C
c) A = C
d) A = B = C

34) Given the sets A = {1,2,3}, B = {3,4}, C = {4,5,6}, then is
a) {3}
b) {1,2,3,4}
c) {1,2,4,5}
d) {1,2,3,4,5,6}

35) Sets A and B have 3 and 6 elements respectively. What can
be the minimum
number of elements in ?

a) 3
b) 6
c) 9
d) 18

36) Two finite sets have m and n elements. The total number of
subsets of the first set is 56
more than the total number
of subsets of the second set. The values of m and n are

a) 7,6
b) 6,3
c) 5,1
d) 8,7

37) The number of proper subsets of the set {1,2,3} is:
a) 8
b) 7
c) 6
d) 5

38) If A, B and C are non-empty sets, then
equals:

a)
b)
c)
d)

39) In a class of 100 students, 55 students have passed in Mathematics
and 67 students have passed in Physics. Then the number of students who have
passed in Physics only is

a) 22
b) 33
c) 10
d) 45

40) Let
and S be the subset of AxB defined by

This defines

a) a one-one function from A into B
b) a many-one function from A into B
c) a bijective mapping from A into B
d) not a function

41) Let A= {a,b,c} and B = {1,2}. Consider a relation R defined
from set A to set B.
Then R is equal to set

a) A
b) B
c) AxB
d) BxA

42) Out of 800 boys in a school. 224 played cricket, 240 played
hockey and 336 played
basketball. Of the total, 64 played
both basketball and hockey; 80 played cricket and
and 40 played cricket and hockey; 24 played all the three games. The number
of boys who did not play any game is

a) 128
b) 216
c) 240
d) 160

43) In a college of 300 students, every student reads 5 newspaper
and every newspaper is read by 60 students. The no. of newspaper is

a) at least 30
b) at most 20
c) exactly 25
d) none of these

44) The number of non-empty subsets of the set {1,2,3,4} is
a) 15
b) 14
c) 16
d) 17

45) A relation from P to Q is
a) a universal set of PxQ
b) PxQ
c) an equivalent set of PxQ
d) a subset of PxQ

46) The set of intelligent students in a class is
a) a null set
b) a singleton set
c) a finite set
d) not a well defined collection

47) If A and B are two given sets, then
is equal to

a) A
b) B
c)
d)

48) If A = [x:x is a multiple of 3) and B = [x:x is a multiple
of 5], then A – B is
(
means complement of A)

a)
b)
c)
d)

49)

In a certain town 25% families own a phone and 15% own a
car, 65% families own
neither a phone nor a car. 2000
families own both a car and a phone.

1. 10% families own both a car and a phone.
2. 35%families own either a car or a phone.
3. 40,000 families live in the town.
Which of the above statements are correct?

a) 1 and 2
b) 1 and 3
c) 2 and 3
d) 1,2 and 3

50) Which of the following is the empty set?
a)
b)
c)
d)

51)

The shaded region in the given figure is

a)
b)
c)
d)

52) If ,
then

a)
b)
c)
d)

53) Let E = {1,2,3,4} and F = {1,2}. Then the number of onto
functions from E to F is

a) 14
b) 16
c) 12
d) 8

54) The number of real solutions of the equation
is

a) 1
b) 2
c) 0
d) none of these

55) Let .
The set of all values of x for which
is real, is

a) [-1, 1]
b)
c)
d)

56)
a)
b)
c) x = y
d) none of the given

57)
a) 15
b) 135
c) 45
d) 90

58)
a) d = bc
b) c = bd
c) b = cd
d) none

59)
a) {3, 6, 9,……….}
b) {5, 10, 15, 20,……..}
c) {15, 30, 45,………}
d) none of these

60) Give the relation R = (1,2) (2, 3) on the set A = ( 1, 2, 3) the minimum number of ordered pairs which when added to R make it an equivalence relation is
a) 5
b) 6
c) 7
d) 8

61) Consider a set A of all determinants of order 3 with entries 0 or 1 only. Let B be the subset of A consisting of all determinants with value. Let C be the subset of all the set of all determinant with value -1 . Then
a) C is empty
b) B has as many elements as C
c) A = B U C
d) B has twice as many elements as C

62) An integer \’m\’ is said to be related to another integer \’n\’ if m is a multiple of n. Then the relation is
a) reflexive and symmetric
b) reflexive and transitive
c) symmetric and transitive
d) equivalence relation

63)
a) an equivalence relation on R
b) reflexive, transitive but not symmetric
c) symmetric , transitive but not reflexive
d) neither transitive nor reflexive but symmetric

64)
a) reflexive
b) symmetric
c) transitive
d) anti symmetric

65)

In the set A = { 1, 2, 3, 4, 5 }, a relation R is defined by R = { x, y / x, y Î
A and x < y } . Then R is

a) reflexive
b) symmetric
c) transitive
d) none of these

66)
a) reflexive
b) symmetric
c) transitive
d) none of these

67)
a) 0
b)
c) f ( x + y )
d) none of these

68)
a)
b)
c)
d)

69)
a) a
b) x
c)

x n

d)

áa n

70)
a)
b)
c)
d) none of these

71)

If  f :  R «
R  be a mapping defined by  f (x)  = x3  + 5,
then  f -1 ( x)  is equal to

a)

( x + 5 )1/3

b)

( x – 5 )1/3

c)

( 5 – x )1/3

d) 5 – x

72)
a) R
b) (0, 1)
c) (1,0)
d) (1, 1)

73)
a)
b)
c)
d)

74) If f (x) = ax + b and g (x) = cx + d, then f (g (x) ) = g (f ( x) ) is equivalent to
a) f (a) = g (c)
b) f (b) = g (b )
c) f (d) = g (b)
d) f (c) = g (a )

75)
a) d = -a
b) d = a
c) a = b = c= d = 1
d) a = b = 1

76)

Let f :  R ®
R  be defined by  f (x)  =  3x – 4  then f -1
(x)  is

a)
b)
c) 3x + 4
d) none

77)
a)
b)

2 n
2

c)

2 n
1

d)

2 n

78)

If f : R ®
R defined by f (x) = x2 + 1, then the value of f -1
(17)and f -1 ( -3 ) respectively are

a)

, (2, -2 )

b)

(3, -3) ,

c)

(4, -4) ,

d)

(4, -4) and (2, -2)

79) f (x) = | sin x | has an inverse if its domain is
a)

( 0 , p
)

b)

( 0, p/2
)

c)

( –  p/4
p/4 )

d) none

80) Let n (U) = 700, n (A) = 200, n (B) = 300 and
n = 100,
then n =

a) 400
b) 600
c) 300
d) 200

81) Suppose are
thirty sets each with five elements and are
n sets each with three elements such that
If each element of S belongs to exactly ten of the
and exactly 9of the
then the value of n is

a) 15
b) 135
c) 45
d) 90

82) If the set has p elements, b has q elements,then
the number of elements in AxB is:

a) p + q
b) p + q +1
c) pq
d)

83) If A and B are two sets such that n(A) = 70, n(B) =60 and
, then
is equal
to

a) 240
b) 50
c) 40
d) 20

84) For two sets
if

a)
b)
c)
d) A = B

85) R is a relation over the set of real numbers and it is given
by mn 0.
Then R is

a) symmetric and transitive
b) reflexive and symmetric
c) a partial order relation
d) an equivalence relation

86) R is a relation over the set of integers and it is given
by .Then
R is

a) reflexive and transitive
b) reflexive and symmetric
c) symmetric and transitive
d) an equivalence relation

87) Let r be a relation over the set N x N and it is defined
by

a) reflexive only
b) symmetric only
c) transitive only
d) an equivalence relation

88) Let A =
If f:
be bijective then a possible
definition of f (x) is

a)
b)
c)
d) none of these

89) Let A =
and B = .
If f is a function from A to B and g is a
one-one function
from A to B then the maximum number of definitions
of
(i) f is 9
(ii) g is 9
(iii) f is 27
(iv) g is 6

a) i and ii
b) ii and iii
c) iii and iv
d) none of these

90) If A = [x : f (x) = 0] and B= [x : g (x) = 0] then
will be

a)
b)
c)
d) none of these

91) Let
Then

a)
b)
c)
d) none of these

92) If the sets A and B are defined as
then

a)
b)
c)
d)

93) If
a)
b)
c) X = Y
d) none of these

94) Let A and B be two non-empty subsets of a set X such that
A is not a subset of B, then

a) A is always a subset of the complement of B
b) B is always a subset of A
c) A and B are always disjoint
d) A and the complement of B are always non-disjoint

95) If the sets A and B are defined as

a)
b)
c)
d) none of these

96) If
then the power set of A is

a) A
b)
c)
d) none of these

97) Which of the following is an even function? Here [.] denotes the greatest
integer function and f is any function.

a) [x]-x
b) f(x) – f(-x)
c)
d) f(x)+f(-x)

98) If
a)
b)
c)
d)

99) If f(x)  is a function of x such that for
all xR the f(x)
is

a)
b)
c) 1- x
d) none of these

100) A set contains 2n +1 elements. The number of sub sets of this set which contains more than n elements is
a)

2 2n

b)

2n

c)

2n+1

d)

22n – 1