Class 12 Maths Chapter 1 Relations and Functions MCQ with Answers

Check the below NCERT MCQ Questions for Class 12 Maths Chapter 1 Relations and Functions with Answers Pdf free download. MCQ Questions for Class 12 Maths with Answers were prepared based on the latest exam pattern. We have provided Relations and Functions Class 12 Maths MCQs Questions with Answers to help students understand the concept very well.

Q.1 Consider the binary operation * on a defined by x * y = 1 + 12x + xy, ∀ x, y ∈ Q, then 2 * 3 equals

(a) 31
(b) 40
(c) 43
(d) None of these

Q.2 Let A = (1, 2, 3). Then the number of equivalence relations containing (1, 2) is

(a) 1
(b) 2
(c) 3
(d) 4

Q.3 The binary operation * defined on N by a * b = a + b + ab for all a, b ∈ N is

(a) commutative only
(b) associative only
(c) both commutative and associative
(d) none of these

Q.4 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

Q.5 The number of commutative binary operation that can be defined on a set of 2 elements is

(a) 8
(b) 6
(c) 4
(d) 2

Q.6 Set A has 3 elements and the set B has 4 elements. Then the number of injective functions that can be defined from set A to set B is

(a) 144
(b) 12
(c) 24
(d) 64

Q.7 Let R be the relation in the set N given by : R = {(a, b): a = b – 2, b > 6}. Then:

(a) (2, 4) ∈ R
(b) (3, 8) ∈ R
(c) (6, 8) ∈ R
(d) (8, 7) ∈ R

Q.8 Let T be the set of all triangles in the Euclidean plane, and let a relation R on T be defined as aRb if a is congruent to b ∀ a, b ∈ T. Then R is

(a) reflexive but not transitive
(b) transitive but not symmetric
(c) equivalence
(d) None of these

Q.9 Let us define a relation R in R as aRb if a ≥ b. Then R is

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

Q.10 A relation S in the set of real numbers is defined as xSy ⇒ x – y+ √3 is an irrational number, then relation S is

(a) reflexive
(b) reflexive and symmetric
(c) transitive
(d) symmetric and transitive

Q.11 The function f : R → R defined by f(x) = 3 – 4x is

(a) Onto
(b) Not onto
(c) None one-one
(d) None of these

Q.12 The function f : A → B defined by f(x) = 4x + 7, x ∈ R is

(a) one-one
(b) Many-one
(c) Odd
(d) Even

Q.13 Let R be a relation on the set N of natural numbers defined by nRm if n divides m. Then R is

(a) Reflexive and symmetric
(b) Transitive and symmetric
(c) Equivalence
(d) Reflexive, transitive but not symmetric

Q.14 The smallest integer function f(x) = [x] is

(a) One-one
(b) Many-one
(c) Both (a) & (b)
(d) None of these

Q.15 Let f : R → R be defined as f(x) = 3x. Then

(a) f is one-one onto
(b) f is many-one onto
(c) f is one-one but not onto
(d) f is neither one-one nor onto

Q.16 The number of binary operations that can be defined on a set of 2 elements is

(a) 8
(b) 4
(c) 16
(d) 64

Q.17 Let A = N × N and * be the binary operation on A defined by (a, b) * (c, d) = (a + c, b + d). Then * is

(a) commutative
(b) associative
(c) Both (a) and (b)
(d) None of these

Q.18 Find the identity element in the set I+ of all positive integers defined by a * b = a + b for all a, b ∈ I+.

(a) 1
(b) 2
(c) 3
(d) 0

Q.19 What type of a relation is R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} on the set A – {1, 2, 3, 4}

(a) Reflexive
(b) Transitive
(c) Symmetric
(d) None of these

Q.20 Let * be a binary operation on set Q – {1} defind by a * b = a + b – ab : a, b ∈ Q – {1}. Then * is

(a) Commutative
(b) Associative
(c) Both (a) and (b)
(d) None of these

Q.21 Let A = {1, 2, 3}. Then number of relations containing {1, 2} and {1, 3}, which are reflexive and symmetric but not transitive is:

(a) 1
(b) 2
(c) 3
(d) 4

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