# Unseen Passage

For Class 4 to Class 12

# Sets MCQ Class 11 Mathematics

Please refer to Chapter 1 Sets MCQ Class 11 Mathematics with answers below. These multiple-choice questions have been prepared based on the latest NCERT book for Class 11 Mathematics. Students should refer to MCQ Questions for Class 11 Mathematics with Answers to score more marks in Grade 11 Mathematics exams. Students should read the chapter Sets and then attempt the following objective questions.

## MCQ Questions Class 11 Mathematics Chapter 1 Sets

The Sets MCQ Class 11 Mathematics provided below covers all important topics given in this chapter. These MCQs will help you to properly prepare for exams.

Question. 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

D

Question. If A = {x : x2 = 1 } and B = {x : x4 = 1} , then AD B is equal to
(a) {i, – i}
(b) {- 1, 1}
(c) {- 1, 1, i, – 1}
(d) None of these

A

Question. The following sets
A = {x : x is an integer, -1/2 <x<9/2 } and B = {x : x is a month of year not having 31 days} is equivalent to
(a) A = {0, 1, 2, 3}, B = {February, April, June, September,November}
(b) A = {0, 1, 2, 3, 4}, B = {February, April, June, September,November}
(c) A = {0, 3, 4}, B = {April, June, September, November}

B

Question. Which of the following is not null set?
(a) Set of odd natural numbers divisible by 2
(b) Set of even prime numbers
(c) {x : x is a natural number, x < 5 and x > 7}
(d) {y : y is a point common to any two parallel lines}

B

Question. Let S = set of points inside the square, T = the set of points inside the triangle and C = the set of points inside the circle. If the triangle and circle intersect each other and are contained in a square. Then,
(a) S ∩ T ∩ C = f
(b) S ∪ T ∪ C = C
(c) S ∪ T ∪ C = S
(d) S T = S ∩ C

C

Question. If A = {x : x = n , n = , , } 2 1 2 3 , then number of proper subsets is
(a) 3
(b) 8
(c) 7
(d) None of these

C

Question. If A and B are non-empty sets, then P(A) P(B) is equal to
(a) P(A ∪ B)
(b) P(A ∩ B)
(c) P(A) = P(B)
(d) None of these

D

Question. If A = {1, 3, 5, 7, 9, 11, 13, 15, 17}, B = {2, 4 , . . . , 18} and N the set of natural numbers is the universal
set, then A ∪ {(A B) ∩ B∪ } is
(a) f
(b) N
(c) A
(d) B

B

Question. If A = {2, 3, 4, 8, 10},B = {3, 4, 5, 10, 12}, C = {4, 5, 6, 12, 14}, then(A ∩ B) (A ∩ C) is equal to
(a) {3, 4, 10}
(b) {2, 8, 10}
(c) {4, 5, 6}
(d) {3, 5, 14}

A

Question. If aN = {an : n ∈ N} and bN ∩ cN = dN, where a, b, c ∈ N and b, c are coprime, then
(a) b = cd
(b) c = bd
(c) d = bc
(d) None of these

C

Question. If A and B are two given sets, then (A ∩ B)( A ∩ C) is equal to
(a) A
(b) B
(c) f
(d) A∩Bc

D

Question. If A = {x : x is an odd natural number} and B = {x : x is a prime number}, then A ∩ B is
(a) odd number
(b) prime number
(c) odd prime number
(d) None of these

C

Question. Let F1 be the set of parallelograms, F2 be the set of rectangles, F3 be the set of rhombuses, F4 be the set of squares and F5 be the set of trapeziums in a plane.
Then, F1 may be equal to
(a) F2 ∩ F3
(b) F3 ∩ F4
(c) F2 ∪ F5
(d) F2 ∪ F3 ∪ F4 ∪ F1

D

Question. Let S = {x : x is a positivemultiple of 3 less than 100}
P = {x : x is a prime number less than 20}. Then, n(S) + n(P) is
(a) 34
(b) 41
(c) 33
(d) 30

B

Question. If A = {x : x = 4n + 1, 2 £ n £ 5}, then number of subsets of A is
(a) 16
(b) 15
(c) 4
(d) None of these

A

Question. Suppose A1, A2, A30 , , . . ., are thirty sets each having 3 elements and B1, B2, Bn , , . . ., are n sets each having 3 elements. Let = =
and each elements of S belongs to exactly 10 of Ai ’ sand exactly

9 of Bj’ s. The value of n is equal to
(a) 15
(b) 3
(c) 45
(d) None of these

C

Question. In a class of 60 students, 25 students play Cricket and 20 students play Tennis, and 10 students play both the games. Then, the number of students who play neither is
(a) 0
(b) 25
(c) 35
(d) 45

B

Question. If A = {x : x is a multiple of 4} and B = {x : x is a multiple of 6}, then A ∩ Bconsists of allmultiples of
(a) 16
(b) 12
(c) 8
(d) 4

B

Question. Let A and B be two non-empty subsets of a set X such that A is not a subset of B, then B
(a) A is always a subset of the complement of
(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

D

Question. Consider the following relations
I. A – B = A – (A ∩ B)
II. A = (A ∩ B) (A – B)
III. A – (B ∪ C) = (A – B) ∪ (A – C)
Which of these is/are correct?
(a) I and III
(b) Only II
(c) II and III
(d) I and II

D

Question. The set (A ∩ B ∪ )∪ (B ∩ C) is equal to
(a) A ∪B ∪ C
(b) A ∪ B
(c) A ∪ C’
(d) A ∩ B

B

Question. Which of the following is an equivalent set?
(a) A = {a, b, c, d}, B = {d, c, b, a}
(b) A = {4, 8, 12, 16}, B = {8, 4, 16, 18}
(c) A = {x : x is a multiple of 10} B = {10, 15, 20, 25, 30, …}
(d) None of the above

A

Question. Two finite sets have mand n elements. The number of subsets of the first set is 112 more than that of the second set. The values of mand n are, respectively
(a) 4, 7
(b) 7, 4
(c) 4, 4
(d) 7, 7

B

Question. Let X be the universal set for sets A and B. If n (A) = 200, n (B) = 300 and n (A ∩ B) = 100, then n (A’ ∩ Ç B’ ) is equal to 300 provided n (X) is equal to
(a) 600
(b) 700
(c) 800
(d) 900

B

Question. In a survey of 200 students of a school, it was found that 120 study Mathematics, 90 study Physics and 70 study Chemistry, 40 study Mathematics and Physics, 30 study Physics and Chemistry, 50 study Chemistry and Mathematics and 20 none of these subjects. The number of students who study all the three subjects is
(a) 30
(b) 20
(c) 22
(d) 25

B

Question. In a committee, 50 people speak French, 20 speak Spanish and 10 speak both Spanish and French. The number of people speak atleast one of these two languages is
(a) 150
(b) 60
(c) 155
(d) None of these

B

Question. In a college of 300 students, every student reads 5 newspaper and every newspaper is read by 60 students. The number of newspaper is
(a) atleast 30
(b) atmost 20
(c) exactly 25
(d) None of these

C

Question. Which of the following is a singleton set?
(a) {x : x < 1, x ∈ I}
(b) {x : x = 5, x ∈ I}
(c) {x : x2 =,I x ∈}
(d) {x : x2 + x + 1 , x ∈ R}

A

Question. If P(A) = P(B), then
(a) A ⊄/ B
(b) B ⊄/ A
(c) A = B
(d) None of these

C

Question. Which sets are subsets of one and another?
A = {x : x ∈ R and x satisfy x x 2 – 8 + 12 = 0}
B = {2, 4, 6}, C = {2, 4, 6, 8, . . .}, D = {6}
(a) D ⊂ A, D ⊂ B and D ⊂ C
(b) A ⊂ D, B ⊂ D and D ⊂ C
(c) D ⊂ A, B ⊂ D and D ⊂ C
(d) None of the above

A

Question. If X = {8n – 7 – 1 : ∈ } and Y = {49n – 49 : n ∈ N}.Then,
(a) X ⊂ Y
(b) Y ⊂ X
(c) X ⊆ Y
(d) X ∩ Y = Φ

C

Question. There are 100 families in a society, 40 families buy newspaper A, 30 families buy newspaper B, 30 families buy newspaper C, 10 families buy newspaper A and B, 8 families buy newspaper Band C, 5 families buy newspaper A and C, 3 families buy newspaper A, B and C, then the number of families who do not buy any newspaper, is
(a) 20
(b) 80
(c) 0
(d) None of these

A

Question. 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 Basketball 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

D

Question. If A = {x, y} then the power set of A is :
(a) {xx, yy}
(b) {Φ, x, y}
(c) {Φ,{x},{2y}}
(d) {Φ,{x},{y},{x,y}}

D

Question. If A and B are finite sets, then which one of the following is the correct equation?
(a) n (A – B) = n (A) – n (B)
(b) n (A – B) = n (B – A)
(c) n (A – B) = n (A) – n (A ∩ B)
(d) n (A – B) = n (B) – n (A ∩ B)
[n (A) denotes the number of elements in A]

C

Question. The set {x : x is a positive integer less than 6 and 3x – 1 is an even number} in roster form is
(a) {1, 2, 3, 4, 5}
(b) {1, 2, 3, 4, 5, 6}
(c) {2, 4, 6}
(d) {1, 3, 5}

A

Question. What does the shaded portion of the Venn diagram given below represent?

(a) (P ∩ Q) ∩ (P ∩ R)
(b) ((P ∩ Q) –R) ∪ ((P ∩ R) –Q)
(c) ((P ∪ Q) –R) ∩ ((P ∩ R) –Q)
(d) ((P ∩ Q) ∪ R) ∩ ((P ∪ Q) –R)

B

Question. Given the sets
A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}. Which of the following may be considered as universal set for all the three sets A, B and C?
(a) {0, 1, 2, 3, 4, 5, 6}
(b) Φ
(c) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
(d) {1, 2, 3, 4, 5, 6, 7, 8}

C

Question. The shaded region in the given figure is

(a) A ∩ (B ∪ C)
(b) A ∪ (B ∩ C)
(c) A ∩ (B – C)
(d) A – (B ∪ C)

D

Question. If A = {a, {b}}, then P(A) equals.
(a) {Φ, {a}, {{b}}, {a, {b}}}
(b) {Φ, {a}}
(c) {{a}, {b}, Φ}
(d) None of these

A

Question. Match the following sets in column -I with the equal sets in column-II.

Codes:
A B C D E F
(a) 5 1 4 3 1 2
(b) 3 4 2 1 5 4
(c) 4 3 5 2 2 1
(d) 1 2 3 4 5 2

C

Question. If A and B are two sets, then A ∩ (A ∪ B)’ is equal to
(a) A
(b) B
(c) Φ
(d) None of these

C

Question. Let X = {1, 2, 3, 4, 5}. Then, the number of elements in X are
(a) 3
(b) 2
(c) 1
(d) 5

D

Question. Which of the following is not a null set?
(a) Set of odd natural numbers divisible by 2
(b) Set of even prime numbers
(c) {x : x is a natural number, x < 5 and x > 7}
(d) {y : y is a point common to any two parallel lines}

B

STATEMENT TYPE QUESTIONS

Question. Statement-I : The Venn diagram of (A ∪ B)’ and A’ ∩ B’ are same.
Statement-II : The Venn diagram of (A ∩ B)’ and A’ ∪ B’ are different.
(a) Statement I is true
(b) Statement II is true
(c) Both are true
(d) Both are false

C

Question. Consider the following sets.
A = {0},
B = {x : x > 15 and x < 5},
C = {x : x – 5 = 0},
D = {x : x2 = 25},
E = {x : x is an integral positive root of the equation
x2 – 2x – 15 = 0}
Choose the pair of equal sets
(a) A and B
(b) C and D
(c) C and E
(d) B and C

C

Question. Consider the following relations:
I. A – B = A – (A ∩ B)
II. A = (A ∩ B) ∪ (A – B)
III. A – (B ∪ C) = (A – B) ∪ (A – C)
Which of these is/are correct?
(a) Both I and III
(b) Only II
(c) Both II and III
(d) Both I and II

D

Question. Statement – I : The set of positive integers greater than 100 is infinite.
Statement – II : The set of prime numbers less than 99 is finite.
(a) Statement I is true
(b) Statement II is true
(c) Both are true
(d) Both are false

C

Question. Suppose A be a non-empty set, then the collection of all possible subsets of set A is a power set P(A).
Which of the following is correct?
I. P(A) ∩ P(B) = P (A ∩ B)
II. P(A) ∪ P(B) = P(A ∪ B)
(a) Only I is true
(b) Only II is true
(c) Both I and II are true
(d) Both I and II are false