# Class 12 Mathematics Chapter 1 Relations and Functions MCQ Questions with Answer

Relations and Functions Class 12 MCQ is one of the best strategies to prepare for the CBSE Class 12 Board exam. If you want to complete a grasp concept or work on one’s score, there is no method except constant practice. Students can improve their speed and accuracy by doing more MCQ on Relations and Functions class 12, which will help them all through their board test.

## Relations and Functions Class 12 MCQ Questions with Answer

Class 12 Maths MCQ with answers are given here to chapter 1 Relations and Functions. These MCQs are based on the latest CBSE board syllabus and relate to the latest Class 12 Mathematics syllabus. By Solving these Class 12 MCQs, you will be able to analyze all of the concepts quickly in the chapter and get ready for the Class 12 Annual exam.

Learn Relations and Functions Class 12 MCQ with answers pdf free download according to the latest CBSE and NCERT syllabus. Students should prepare for the examination by solving CBSE Class 12 Mathematics Relations and Functions MCQ with answers given below.

Question 1. Let A = {1, 2, 3} and consider the relation R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)}. Then R is
(a) reflexive but not symmetric
(b) reflexive but not transitive
(c) symmetric and transitive
(d) neither symmetric nor transitive

A

Question 2. For real numbers x and y, define xRy if and only if x – y + 2 is an irrational number. Then the relation R is
(a) reflexive
(b) symmetric
(c) transitive
(d) none of these

A

Question 3. The maximum number of equivalence relation on the set A = {1, 2, 3} are
(a) 1
(b) 2
(c) 3
(d) 5

D

Question 4. Let f : R → R be defined by f(x) = sin x and g : R → R be defined by g(x) = x2, then fog is
(a) x2 sin x
(b) (sin x)2
(c) sin x2
(d) sinx/x2

C

Question 5. Let A and B be finite sets containing m and n elements respectively. The number of relations that can be defined from A to B is
(a) 2mn
(b) 2m+n
(c) mn
(d) 0

A

Question 6. Let f : R → R be the functions defined by f(x) = x3 + 5. Then f–1(x) is
(a) (x 5) 1/3
(b) (x – 5) 1/3
(c) (5 – x) 1/3
(d) 5 – x

B

Question 7. Let A = {1, 2, 3}. Then number of equivalence relations containing (1, 2) is/are
(a) 1
(b) 2
(c) 3
(d) 4

B

Question 8. 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

D

Question 9. If f(x) = sin2 x and the composite function g(f(x)) = |sin x|, then g(x) is equal to
(a) √x + 1
(b) √x – 1
(c) √x
(d) –√x

C

Question 10. Set A has 3 elements and the set B has 4 elements. Then the number of injective mapping that can be defined from A to B is
(a) 144
(b) 12
(c) 24
(d) 64

C

Question 11. Let f : R –{3/5 R be defined by f (x) = 3x+2 /5x–3. Then
(a) f –1(x) = f(x)
(b) f –1(x) = – f(x)
(c) fo f(x) = – x
(d) f-1 (x) 1/19 f (x)

A

Question 12. If the set A contains 5 elements and the set B contains 6 elements, then the number of one-one and onto mapping from A to B is
(a) 720
(b) 120
(c) 0
(d) none of these

C

Question 13. If A = {a, b, c, d}, then a relation R = {(a, b), (b, a), (a, a)} on A is
(a) symmetric only
(b) transitive only
(c) reflexive and transitive
(d) symmetric and transitive only

D

Question 14. The function f : R → R defined by f(x) = 2x + 2|x| is
(a) One-one and onto
(b) Many-one and onto
(c) One-one and into
(d) Many-one and into

C

Question 15. The relation R in the set A = {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)} is
(a) reflexive and symmetric but not transitive
(b) reflexive and transitive but not symmetric
(c) symmetric and transitive but not reflexive
(d) an equivalence relation

B

Question 16. Consider the non-empty set consisting of children in a family and a relation R defined as aRb if a is brother of b. Then R is
(a) symmetric but not transitive
(b) transitive but not symmetric
(c) neither symmetric nor transitive
(d) both symmetric and transitive

B

Question 17. Which of the following functions from z into z is bijection?
(a) f(x) = x3
(b) f(x) = x + 2
(c) f(x) = 2x + 1
(d) f(x) = x2 + 1

B

Question 18. Let f : R → R be defined by f(x) = x2 + 1. Then, pre-images of 17 and –3, respectively, are
(a) f, {4, –4}
(b) {3, –3}, f
(c) {4, –4}, f
(d) {4, –4}, {2, –2}

C

Question 19. 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 symmetri

D

Question 20. Let f : [2, ∞) → R be the function defined by f(x) = x2 – 4x + 5, then the range of f is
(a) R
(b) [1, ∞)
(c) [4, ∞)
(d) [5, ∞)

B

Question 21. If a relation R on the set {1, 2, 3} be defined by R = {(1, 2)}, then R is
(a) reflexive
(b) transitive
(c) symmetric
(d) none of these

B

Question 22. Let L denotes the set of all straight lines in a plane. Let a relation R be defined by lRm if and only if l is perpendicular to m ∀ l, m ∈ L. Then R is
(a) reflexive
(b) symmetric
(c) transitive
(d) none of these

B

Question 23. If A = {1, 2, 3}, B = {1, 4, 6, 9} and R is a relation from A to B defined by ‘x is greater than y’.
Then range of R is
(a) {1, 4, 6, 9}
(b) {4, 6, 9}
(c) {1}
(d) none of these

C

Question 24. Let f : R → R be defined by f(x) = 3x – 4. Then f –1(x) is given by
(a) (x +4)/3
(b) x/3– 4
(c) 3x + 4
(d) none of these

A

Question 25. Let f : R → R be defined by f(x) = 3x2 – 5 and g : R → R by g(x) = x /x2 + 1 . Then gof is
(a) 3x2 –5 /9x4 –30x2 + 26
(b) 3x2 –5 /9x–6x2 + 26
(c) 3x2 /x4 –2x2 – 4
(d) 3x2 /9x4 –30x2 – 2

A

Whoever needs to take the CBSE Class 12 Board Exam should look at this MCQ. To the Students who will show up in CBSE Class 12 Mathematics Board Exams, It is suggested to practice more and more questions. Aside from the sample paper you more likely had solved. These Relations and Functions class 12 MCQ are ready by the subject specialists themselves.

## Fill in the Blanks

Question 1. If any set A contains n elements. Then, the total number of injective functions from A onto itself is _________ .

n!

Question 2. A relation from a set A to a set B is a ___________ of A × B.

Subset

Question 3. The domain of the function f : R → R defined by f (x) = x2 – 3x + 2 is ___________ .

(– ∞, 1] ∪ [2, ∞)

Question 4. If f(x) = {4 – (x – 7)3}, then f –1(x) = ___________ .

7 (4 – x) 1/3

Question 5. A relation R from set A to set B is said to be ___________ if R = A × B.

The universal relation

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