c) Collection of objects with a common fixed property.

Ans: d

Q 2) If A, B and C are any three sets, then A – (B ∪ C) is equal to

(a) (A – B) ∪ (A – C)

(b) (A – B) ∪ C

(c) (A – B) ∩ C

(d) (A – B) ∩ (A – C)

Ans: d

Q 3) A set is known by its

a) Elements

b) values

c) Members

d) Letters

Ans: a

Q 4) (A’)’ = ?

(a) ∪ – A

(b) A

(c) ∪

(d) A’

Ans: b

Q 5) There are 230 students. 80 play football, 42 play soccer and 12 play rugby. 32 play exactly 2 sports and 4 play all three. How many students play none?

a) 132

b) 136

c) 140

d) 94

Ans: b

Q 6) In a group of 60 people, 27 like cold drinks and 42 like hot drinks and each person like at least one of the two drinks. How many like both coffee and tea?

a) 30

b) 15

c) 14

d) 9

Ans: d

Q 7) IF A = [5, 6, 7] and B = [7, 8, 9] then A ∪ B is equal to

(a) [5, 6, 7, 8, 9]

(b) [5, 6, 7]

(c) [7, 8, 9]

(d) None of these

Ans: a

Q 8) The members of the set S = {x | x is the square of an integer and x < 100} is

(a) {0, 2, 4, 5, 9, 58, 49, 56, 99, 12}

(b) {0, 1, 4, 9, 16, 25, 36, 49, 64, 81}

(c) {1, 4, 9, 16, 25, 36, 64, 81, 85, 99}

(d) {0, 1, 4, 9, 16, 25, 36, 49, 64, 121}

Ans: b

Q 9) Number of subsets of a set of order three is

a) 3

b) 6

c) 8

d) 9

Ans: c

Q 10) If A, B, C be three sets such that A ∪ B = A ∪ C and A ∩ B = A ∩ C, then,

(a) B = C

(b) A = C

(c) A = B = C

(d) A = B

Ans: a

Q 11) Order of the power set of a set of order n is

a) n

b) 2^{n}

c) n^{2}

d) 2n

Ans: b

Q 12) Empty set is a?

(a) Infinite Set

(b) Invalid Set

(c) None of the above

(d) Finite Set

Ans: d

Q 13) The number of elements in the power set of the set {{a, b}, c} is

a) 8

b) 4

c) 3

d) 7

Ans: b

Q 14) Which of the following two sets are equal?

(a) A = {1, 2} and B = {1}

(b) A = {1, 2} and B = {1, 2, 3}

(c) A = {1, 2, 3} and B = {2, 1, 3}

(d) A = {1, 2, 4} and B = {1, 2, 3}

Ans: c

Q 15) If A and B are two sets such that n(A) = 70, n(B) = 60 and n(A U B) = 110, then n(A ⋂ B) = ?

a) 240

b) 50

c) 40

d) 20

Ans: d

Q 16) In a class of 50 students, 10 did not opt for math, 15 did not opt for science and 2 did not opt for either. How many students of the class opted for both math and science.

(a) 24

(b) 25

(c) 26

(d) 27

Ans: d

Q 17) In a city of 1000 population, all people read newspaper. 600 people read Hindustan Times and 700 people read Times of India. How many people read only Times of India?

a) 200

b) 400

c) 600

d) 700

Ans: b

Q 18) Which of the following sets are null sets?

a) {0}

b) Ø

c) { }

d) Both (b) & (c)

Ans: d

Q 19) If the number of elements in a set S are 5. Then find the number of elements of the power set P(S) are ?

a) 5

b) 6

c) 16

d) 32

Ans: d

Explanation Number of elements in the power set P(S) = 2^{5} = 32

Q 20) Every set is ___________ of itself

a) Proper subset

b) Improper Subset

c) Compliment

d) None of these

Ans: b

Q 21) The number of non empty subsets of {a, b, c, d} is

a) 3

b) 4

c) 15

d) 16

Ans: c

Q 22) The smallest set A such that A U{1, 2} = { 1, 2, 3, 5, 9} is

a) {3, 5, 9}

b) {2, 3, 5)

c) {1, 2, 5, 9}

d) None of these

Ans: a

Q 23) If A = {5, 6, 7} and {7, 8, 9} then A U B is equal to

a) {5, 6, 7}

b) {5, 6, 7, 8, 9}

c) {7, 8, 9}

d) None of these

Ans: b

Q 24) How many rational and irrational numbers are possible between 0 and 1 ?

a) 0

b) Finite

c) Infinite

d) 1

Ans: c

Q 25) If A = {1, 3, 5, B} and B = {2, 4}, then which of the following is true

a) {1, 2} ⊂ A

b) {2, 4} ⊂ A

c) B ⊂ A

d) None of these

Ans: d

Q 26) If A ={ 1, 2, 3, 4, 5}, then number of proper subsets of A is

a) 120

b) 30

c) 31

d) 32

Ans: c

Q 27) A and B are two sets such that n(A) = 16, n(B) = 14, n(A⋃B) = 25, Then A⋂B is

a) 30

b) 50

c) 5

d) None of these

Ans: c

Q 28) If A and B are two sets in the same universal set. Then A – B =

a) A⋂B

b) A'⋂B

c) A⋂B'

d) None of these

Ans: c

Q 29) n(A) = 20, n(A⋃B) = 42 and n(A⋂B) = 4, then n(B - A) =

a) 22

b) 26

c) 16

d) None of these

Ans: a

Q 30) For any sets A and B : (A⋂B) ⋂ (A - B)

a) A⋂B

b) A - B

c) B

d) A

Ans: d

Q 31) If set A is equal to set B then

a) A ⊂ B

b) B ⊂ A

c) A ⊂ B and B ⊂ A

d) neither A ⊂ B nor B ⊂A

Ans: c

Q 32) Let A= {2, 3, 5} and B = {3, 5, 7}. Which of the following is true?

a) A ⊂ B

b) B ⊂ A

c) A = B

d) A ⊂ A

Ans: d

Q 33) Let X be set of rational numbers. Which of the following is superset of X?

a) Set of real numbers

b) Set of natural numbers

c) Set of whole numbers

d) Set of integers

Ans: a

Q 34) Let A = {1, 2, {3, 4}, 5}. Which of the following is not true?

a) {3, 4} ⊂ A

b) {3, 4} ∈ A

c) {{3, 4}} ⊂ A

d) {1, 2, 5} ⊂ A

Ans: a

Q 35) The total number of subsets of a finite set containing n elements is?

a)
2^{n+1}

b) 2n

c) 2^{n}

d) N

Ans: c

Q 36) If set A = {1, 2, 3, 4} and B = {3, 4, 5, 6}. Find B - A.

a) {1, 2, 3, 4, 5, 6}

b) {3, 4}

c) {1, 2}

d) {5, 6}

Ans: d

Q 37) If set A has 10 elements, set B has 20 elements, 5 elements are common to both then find the number of elements in X∪Y.

a) 10

b) 15

c) 20

d) 25

Ans: d

Q 38) In a city of 1000 population, all people read newspaper. 600 people read Hindustan Times and 700 people read Times of India. How many people read both newspapers?

a) 100

b) 300

c) 1000

d) 1300

Ans: b

Q 39) In a family of 10 members, 7 of them like tea or coffee, 4 of them like tea and 5 of them like coffee. How many of them like both tea and coffee?

a) 1

b) 2

c) 7

d) 9

Ans: b

Q 40) In a city of 1000 population, all people read newspaper. 600 people read Hindustan Times and 700 people read Times of India. How many people read only Hindustan Times?

a) 100

b) 200

c) 300

d) 600

Ans: c

Q 41) Sets A and B have 3 and 6 elements respectively. What can be the minimum number of elements in A U B.

a. 9

b. 18

c. 3

d. 6

Ans: d

Q 42) Let the set A = {x : x is a letter in the word "INTELLIGENT"}, then the number of subsets of A is:

a) 2^{11}

b) 2^{11 }- 1

c) 64

d) 63

Ans: d

Q 43) A null set is denoted by :

a) {x : x = x}

b) Φ

c) {x : x ≠ x}

d) {0}

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Excellent work

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