Below you will find **MCQ Questions of Chapter 1 Relations and Functions Class 12 Maths Free PDF Download** that will help you in gaining good marks in the examinations and also cracking competitive exams. These Class 12 MCQ Questions with answers will widen your skills and understand concepts in a better manner.

# MCQ Questions for Class 12 Maths Chapter 1 Relations and Functions with answers

1. Let f : N→ R - {0} defined as f(x) = 1/x where x ∈ N is not an onto function. Which one of the following sets should be replaced by N such that the function f will become onto? (where R_{0} = R - {0})

(a) R_{0}

(b) W

(c) Z

(d) None of these

► (a) R_{0}

2. R = {(1, 1), (2, 2), (1, 2), (2, 1), (2, 3)} be a relation on A = {1, 2, 3}, then R is

(a) Symmetric

(b) Anti symmetric

(c) Not antisymmetric

(d) Reflexive

► (c) Not antisymmetric

3. If f: A→B and g:B→C are onto, then gof: A→C is:

(a) A many-one and onto function

(b) A bijective function

(c) An into function

(d) An onto function

► (d) An onto function

4. Let a relation T on the set R of real numbers be T = {(a, b) : 1 + ab < 0, a, ∈ R}. Then from among the ordered pairs (1, 1), (1, 2), (1, -2), (2, 2), the only pair that belongs to T is_____.

(a) (2, 2)

(b) (1, 1)

(c) (1, -2)

(d) (1, 2)

► (c) (1, -2)

5. How many onto functions from set A to set A can be formed for the set A = {1, 2, 3, 4, 5, ……n}?

(a) n^{2}

(b) n

(c) n!

(d) 2n

► (c) n!

6. The range of the function f(x) = [sin x] is

(a) [1, 1].

(b) (–1, 1)

(c) {– 1, 0, 1}

(d) {–1, 1}

► (c) {– 1, 0, 1}

7. Let R be the relation on the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3,3), (3,2)}. then R is

(a) R is reflexive and symmetric but not transitive.

(b) R is symmetric and transitive but not reflexive.

(c) R is an equivalence relation.

(d) R is reflexive and transitive but not symmetric.

► (d) R is reflexive and transitive but not symmetric.

8. Let T be the set of all triangles in a plane with R a relation in T given by R = {(T_{1}, T_{2}) : T_{1} is congruent to T_{2}}. Then R is

(a) Non commutative relation

(b) A universal relation

(c) An equivalence relation

(d) An empty relation

► (c) An equivalence relation

9. R is a relation from { 11, 12, 13} to {8, 10, 12} defined by y = x – 3. The relation R^{−1}

(a) {(8, 11), (9, 12), (10, 13)}

(b) {(11, 8), (13, 10)}

(c) {(8, 11), (10, 13)}

(d) None of these

► (c) {(8, 11), (10, 13)}

10. Let A = {a,b,c} and B = {1,2,3} and f: A→B is defined by f={(a,2), (b,1), (c,3)}. Find f^{-1}

(a) {(2,a),(1,b), (3, c)}

(b) Can not be inverted as it is not one-one

(c) Can not be inverted as it is not onto

(d) {(a,2), b,1), (c,3)}

► (a) {(2,a),(1,b), (3, c)}

11. Let C = {(a, b): a^{2} + b^{2} = 1; a, b ∈ R} a relation on R, set of real numbers. Then C is

(a) Equivalence relation

(b) Reflexive

(c) Transitive

(d) Symmetric

► (d) Symmetric

12. If ƒ(x) = tan^{-1} x and g(x) = tan(x), then (gof)(x) =

(a) tan^{-1}xtan(x)

(b) tan^{-1}xcot(x)

(c) x

(d) tan^{-1}xsin(x)

► (c) x

13. If A = {1, 2, 3, 4} and B = {1, 3, 5} and R is a relation from A to B defined by(a, b) ∈ element of R ⇔ a < b. Then, R = ?

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

(b) {(1, 3), (1, 5), (2, 3), (2, 5), (3, 5), (4, 5)}

(c) {(2, 3), (4, 5), (1, 3), (2, 5), (5, 3)}

(d) {(5, 3), (3, 5), (5, 4), (4, 5)}

► (b) {(1, 3), (1, 5), (2, 3), (2, 5), (3, 5), (4, 5)}

14. If f : A → B and g : B → C be two functions. Then, composition of f and g, gof : A → C is defined a

(a) (gof)(x) = f(g(x)), for all x ∈ A

(b) (gof)(x) = g(f(x)), for all x ∈ A

(c) (gof)(x) = g(x), for all x ∈ A

(d) None of the above

► (b) (gof)(x) = g(f(x)), for all x ∈ A

15. Given the relation R = {(1, 2), (2, 3)} on eht set {1, 2, 3}, the minimum number of ordered pairs which when added to R make it an equivalence

(a) 5

(b) 6

(c) 8

(d) 7

► (d) 7

16. Let R be a relation on N, set of natural numbers such that m R n ⇔ m divides n. Then R is

(a) Reflexive and symmetric

(b) Neither reflexive nor transitive

(c) Reflexive and transitive

(d) Symmetric and transitive

► (c) Reflexive and transitive

17. Number of relations that can be defined on the set A = {a, b, c, d} is

(a) 2^{4}

(b) 4^{4}

(c) 16

(d) 2^{16}

► (d) 2^{16}

18. Let A = {1, 2, 3, 4, 5, 6, 7}. P = {1, 2}, Q = {3, 7}. Write the elements of the set R so that P, Q and R form a partition that results in equivalence relation.

(a) {4, 5, 6}

(b) {0}

(c) {1, 2, 3, 4, 5, 6, 7}

(d) { }

► (a) {4, 5, 6}

19. A function f: A x B → B x A defined by f (a, b) = (b, a) on two sets A and B. The function is:

(a) Many-one

(b) One-one but not onto

(c) One-one and onto

(d) Neither one-one nor onto

► (c) One-one and onto

20. If ƒ(x) = xsecx, then ƒ(0) =

(a) −1

(b) 0

(c) 1

(d) √(2)

► (b) 0

21. Which one of the following relations on set of real numbers is an equivalence relation?

(a) a R b ⇔ a ≥ b

(b) a R b ⇔ |a| = |b|

(c) a R b ⇔ a > b

(d) a R b ⇔ a < b

► (b) a R b ⇔ |a| = |b|

22. Let R be a relation on N (set of natural numbers) such that (m, n) R (p, q) mq(n + p) = np(m + q). Then, R is

(a) An Equivalence Relation

(b) Only Reflexive

(c) Symmetric and reflexive

(d) Only Transitive

► (c) Symmetric and reflexive

Hope the given MCQ Questions will help you in cracking exams with good marks. These **Relations and Functions MCQ Questions** will help you in practising more and more questions in less time.