# MCQs for Mathematics Class 11 with Answers Chapter 1 Sets

Students of class 11 Mathematics should refer to MCQ Questions Class 11 Mathematics Sets with answers provided here which is an important chapter in Class 11 Mathematics NCERT textbook. These MCQ for Class 11 Mathematics with Answers have been prepared based on the latest CBSE and NCERT syllabus and examination guidelines for Class 11 Mathematics. The following MCQs can help you to practice and get better marks in the upcoming class 11 Mathematics examination

## Chapter 1 Sets MCQ with Answers Class 11 Mathematics

MCQ Questions Class 11 Mathematics Sets with answers provided below have been prepared by expert teachers of grade 11. These objective questions with solutions are expected to come in the upcoming Standard 11 examinations. Learn the below provided MCQ questions to get better marks in examinations.

Question. If P(A) denotes the power set of A and A is the void set,then what is number of elements in P{P{P{P(A)}}}?
(a) 0
(b) 1
(c) 4
(d) 16

D

Question. On the set N of all natural numbers define the relationR by aRb iff the g.c.d. of a and b is 2, then R is
(a) reflexive but not symmetric
(b) symmetric only
(c) reflexive and transitive
(d) equivalence relation

B

Question. If A, B and C are three sets such that A ∩ B = A ∩ C and A ∪ B = A ∪ C, then
(a) A = C
(b) B = C
(c) A ∩ B = f
(d) A = B

B

Question. Let R be a relation defined by R = {(4, 5), (1, 4), (4, 6), (7, 6), (3, 7)}, then R-1 OR is
(a) {(1, 1), (4, 4), (4, 7), (7, 4), (7, 7), (3, 3)}
(b) {(1, 1), (4, 4), (7, 7), (3, 3)}
(c) {(1, 5), (1, 6), (3, 6)}
(d) None of the above

A

Question. If n(A) =1000, n(B) = 500, n(A ∩B) ³1 and n(A ∪B) = P, then
(a) 500 £ P £ 1000
(b) 1001£ P £ 1498
(c) 1000 £ P £ 1498
(d) 1000 £ P £ 1499

D

Question. Let A be a non-empty set of real numbers and f : A → A be such that f (f (x )) = x, ” x ÎR. Then, f (x ) is
(a) a bijection
(b) one-one but not onto
(c) onto but not one-one
(d) neither one-one nor onto

A

Question. If n(A) = 4, n(B) = 3, n(A ´B ´C) = 24, then n(C) is equal to
(a) 2
(b) 288
(c) 12
(d) 1

A

Question. If R = {(3, 3) ,(6, 6), (9, 9), (12,12) , (6,12), (3, 9), (3,12),(3, 6)} is a relation on the set A = {3, 6, 9,12}.
The relation is
(a) an equivalence relation
(b) reflexive and symmetric
(c) reflexive and transitive
(d) only reflexive

C

Question. If g(x ) =1 + √x and f {g(x )} = 3 + 2√x + x , then f (x ) is equal to
(a) 1 2 + x2
(b) 2 + x2
(c) 1 + x
(d) 2 + x

B

Question. Let R be the real line. Consider the following subsets of the plane R ´R.
S = {(x, y ): y = x + 1and0 < x < 2}
and T = {(x, y ): x – y is an integer}
Which one of the following is true?
(a) T is an equivalence relation on R but S is not
(b) Neither S nor T is an equivalence relation on R
(c) Both S and T are equivalence relations on R
(d) S is an equivalence relation on R but T is not

Question. Let f (x ) = ax + b and g(x ) = cx + d,a ¹ 0,c ¹ 0. Assume a =1,b = 2, if ( fog) (x ) = ( gof ) (x ) for all x. What can you say about c and d?
(a) c and d both arbitrary
(b) c = 1and d is arbitrary
(c) c is arbitrary and d = 1
(d) c = 1, d =1

Question. If R is relation from {11,12,13} to {8,10,12} defined by y = x – 3. Then, R-1 is
(a) {(8, 11), (10, 13)}
(b) {(11, 18), (13, 10)}
(c) {(10, 13), (8, 11)}
(d) None of these

Question. If X n n N = {4n – 3 -1: Î } andY = {9(n -1) :n ÎN};where N is the set of natural numbers,then X ∪Y is equal to
(a) N
(b) Y-X
(c) X
(d) Y

Question. The function f satisfies the functional equation 3f(X) + 2f (X+59/X-1) = 10X + 30 for all real x ¹1. The value of f (7) is
(a) 8
(b) 4
(c) – 8
(d) 11

Question. If two sets A and B are having 99 elements in common, then the number of elements common to each of the sets A x B and B x A are
(a) 299
(b) 992
(c) 100
(d) 18

Question. The number of onto mapping from the set A = {1, 2, …100} to set B = {1, 2} is
(a) 2100 -2
(b) 2100
(c) 299 -2
(d) 299

Question. Let A = {1, 2, 3, 4}, B = {2, 4, 6}. Then the number of sets C such that A ÇB Í C Í A ÈB is
(a) 6
(b) 9
(c) 8
(d) 10

Question. Let f :R – {n} → R be a function defined by f (x) = x – m/x – n, – wherem M≠n . Then,
(a) f is one-one onto
(b) f is one-one into
(c) f is many-one onto
(d) f is many-one into

Question. Let f :N → N defined by f (x ) = x 2 + x + 1, x ÎN, then f is
(a) one-one onto
(b) many-one onto
(c) one-one but not onto
(d) None of these

Question. Let R = {(x, y ) : x, y ÎN and x2- 4xy + 3y = 0}, where N is the set of all natural numbers. Then, the relationR is
(a) reflexive but neither symmetric nor transitive
(b) symmetric and transitive
(c) reflexive and symmetric
(d) reflexive and transitive

A

Question. Consider the following relations
R = {(x, y) | x and y are real numbers and x = wy for some rational number w};
S = {(m/n , p/q)} and q are integers such that, qm/pn ≠ 0 and qm = pn}. Then,
(a) R is an equivalence relation but S is not an equivalence relation
(b) neither R nor S is an equivalence relation
(c) S is an equivalence relation but R is not an equivalence relation
(d) R and S both are equivalence relations

C

Question. If f(x) + 2f(1/x) = 3x, x≠ 0 and S = {x ÎR : f (x ) = f (- x )}; then S
(a) is an empty set
(b) contains exactly one element
(c) contains exactly two elements
(d) contains more than two elements

C

Question. is equal to
(a) R – {0}
(b) R – {0, 1, 3}
(c) R – – – { , , } 0 1 3
(d) R – – – {0-1, -3, 1/2}

C

Question. Given 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) 7
(c) 6
(d) 8

B

Question. The set (A ∪ B ∪ C) ∩ (A ∩ B’∩ C∩ )’ ∩ C’ is equal to
(a) B C’
(b) A C
(c) B’ C’
(d) None of these

A

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¢ ∩ B¢) is equal to 300 provided n(X ) is equal to
(a) 600
(b) 700
(c) 800
(d) 900

B

Question. If A andB are two sets and A∪B∪C =U. Then, {(A -B)∪(B -C)∪(C – A)}¢ is equal to
(a) A ∪ B ∪ C
(b) A ∪ (B ∩ C)
(c) A ∩ B ∩ C
(d) A ∩ (B ∪ C)

C

Question. Suppose f is a function satisfying f (x + f (x )) = 4f (x ) and f (1) = 4. The value of f (21) is
(a) 16
(b) 64
(c) 4
(d) 44

B

Question. Let A = {(1, 2), (3, 4), 5}, then which of the following is incorrect?
(a) {3, 4} ∉ A as (3, 4) is an element of A
(b) {5}, {(3, 4)} are subsets of A but not elements of A
(c) {1, 2}, {5} are subsets of A
(d) {(1, 2), (3, 4), 5} are subset of A

C

Question. If Φ denotes the empty set, then which one of the following is correct ?
(a) Φ ∈ Φ
(b) Φ ∈ {Φ}
(c) {Φ} ∈ {Φ}
(d) 0 ∈ Φ

B

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

C

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

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

C

Question. The number of non-empty subsets of the set {1, 2, 3, 4} is 3 x a. The value of ‘a’ is
(a) 3
(b) 4
(c) 5
(d) 6

C

Question. The set builder form of given set A = {3, 6, 9, 12} and
B = {1, 4, 9, ….., 100} is
(a) A = {x : x = 3n, n ∈ N and 1 ≤ n ≤ 5},
B = {x : x = n2, n ∈ N and 1 ≤ n ≤ 10}
(b) A = {x : x = 3n, n ∈ N and 1 ≤ n ≤ 4},
B = {x : x = n2, n ∈ N and 1 ≤ n ≤ 10}
(c) A = {x : x = 3n, n ∈ N and 1 ≤ n ≤ 4},
B = {x : x = n2, n ∈ N and 1 < n < 10}
(d) None of these

B

Question. If A = {x : x = n2, n = 1, 2, 3}, then number of proper subsets is
(a) 3
(b) 8
(c) 7
(d) 4

C

Question. Let U be the set of all boys and girls in school. G be the set of all girls in the school. B be the set of all boys in the school and S be the set of all students in the school who take swimming. Some but not all students in the school take swimming.

B

Question. A survey of 500 television viewers produced the following information, 285 watch football, 195 watch hockey, 115 watch basket-ball, 45 watch football and basket ball, 70 watch football and hockey, 50 watch hockey and basket ball, 50 do not watch any of the three games. The number of viewers, who watch exactly one of the three games are
(a) 325
(b) 310
(c) 405
(d) 372

A

Question. Let S = the set of all triangles, P = the set of all isosceles triangles, Q = the set of all equilateral triangles, R = the set of all right-angled triangles. What do the sets P ∩ Q and R – P  represents respectively ?
(a) The set of isosceles triangles; the set of non- isosceles right angled triangles
(b) The set of isosceles triangles; the set of right angled triangles
(c) The set of equilateral triangles; the set of right angled triangles
(d) The set of isosceles triangles; the set of equilateral triangles

A

Question. In the Venn diagram, the shaded portion represents

(a) complement of set A
(b) universal set
(c) set A
(d) None of these

A

STATEMENT TYPE QUESTIONS

Question. Statement-I : If A, B and C are finite sets, then n(A ∪ B ∪ C) = n(A) + n(B) + n(C) – n(A ∩ B) – n(B ∩ C) – n(A ∩ C) + n(A ∩ B ∩ C).
Statement-II : If A, B and C are mutually pairwise disjoint, then n(A ∪ B ∪ C) = n(A) + n(B) + n(C) – n(A ∩ B) – n(B ∩ C) – n(A ∩ C).
(a) Statement I is true
(b) Statement II is true
(c) Both are true
(d) Both are false

A

Question. Statement – I : In the union of two sets A and B, the common elements being taken only once.
Statement – II : The symbol ‘∩’ is used to denote the union.
(a) Statement I is true
(b) Statement II is true
(c) Both are true
(d) Both are false

A

Question. Which of the following is correct?
I. Number of subsets of a set A having n elements is equal to 2n.
II. The power set of a set A contains 128 elements then number of elements in set A is 7.
(a) Only I is true
(b) Only II is true
(c) Both I and II are true
(d) Both I and II are false

C

Question. I. The collection of all months of a year beginning with the letter J.
II. The collection of ten most talented writers of India.
III. A team of eleven best cricket batsmen of the world.
IV. The collection of all boys in your class.
Which of the above are the sets?
(a) I and II
(b) I and III
(c) I and IV
(d) I, II and III

C

Question. Let A = {3, 6, 9, 12, 15, 18, 21}
B = {4, 8,12, 16, 20}
C = {2, 4, 6, 8, 10, 12, 14, 16}
and D = {5, 10, 15, 20}
Which of the following is incorrect?
I. A – B = {4, 8, 16, 20}
II. (C – B) ∩ (D – B) = Φ
III. B – C ≠ B – D
(a) Only I & II
(b) Only II & III
(c) Only III & I
(d) None of these