These Relations And Functions MCQ And Answers are most important for your upcoming examinations including JEE Main & JEE Advanced. These Relations And Functions MCQ And Answers will help you to score good marks in your exams by helping you to prepare the concepts better and hence, help you to understand the concepts more clearly.

## Relations And Functions MCQ And Answers

1. 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) neither transitive nor reflexive but symmetric

(D) symmetric, transitive but not reflexive

**Answer:** reflexive, transitive but not symmetric

2. If the set A contains 5 elements and the set B contains 6 elements, then the number of one-one and onto mappings from A to B is

(A) 720

(B) 120

(C) 0

(D) None of these

**Answer:** 0

3. Which of the following functions from Z into Z are bijective?

(A) f(x) = x³

(B) f(x) = x + 2

(C) f(x) = 2x + 1

(D) f{x) = x² + 1

**Answer:** f(x) = x + 2

4. For real numbers x and y, we write xRy ⇔ x – y + √2 is an irrational number. Then, the relational R is

(A) Reflexive

(B) Symmetric

(C) Transitive

(D) None of these

**Answer:** Reflexive

5. Let R be an equivalence relation on a finite set A having n elements. Then, the number of ordered pairs in R is

(A) Less than n

(B) Greater than or equal to n

(C) Less than or equal to n

(D) None of these

**Answer:** Greater than or equal to n

6. The relation R = {(1,1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)} on set A = {1, 2, 3} is

(A) Reflexive but not symmetric

(B) Reflexive but not transitive

(C) Symmetric and transitive

(D) Neither symmetric nor transitive

**Answer:** Reflexive but not symmetric

7. Let f : R → R be defined by f (x) = 1/x ∀ x ∈ R. Then f is

(A) one-one

(B) onto

(C) bijective

(D) f is not defined

**Answer:** f is not defined

8. 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

**Answer:** None of these

9. Consider the non-empty set consisting of children is 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

**Answer:** transitive but not symmetric

10. 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

**Answer:** reflexive but not symmetric

11. If f: R → R defined by f(x) = 2x + 3 then f^{-1}(x) =

(A) 2x – 3

(B) x-3/2

(C) x+3/2

(D) None of these

**Answer:** x-3/2

12. f: A → B will be an into function if

(A) range (f) ⊂ B

(B) f(a) = B

(C) B ⊂ f(a)

(D) f(b) ⊂ A

**Answer:** range (f) ⊂ B

13. If f : R → R such that f(x) = 3x then what type of a function is f?

(A) one-one onto

(B) many one onto

(C) one-one into

(D) many-one into

**Answer:** one-one into

14. The maximum number of equivalence relations on the set A = {1, 2, 3} are

(A) 1

(B) 2

(C) 3

(D) 5

**Answer:** 5

15. Let f: N → R be the function defined by f(x) = 2x−1/2 and g: Q → R be another function defined by g (x) = x + 2. Then (g 0 f) 3/2 is

(A) 1

(B) 0

(C) 7/2

(D) None of these

**Answer:** None of these

16. If f: R → R such that f(x) = 3x – 4 then which of the following is f^{-1}(x)?

(A) 1/3 (x + 4)

(B) 1/3 (x – 4)

(C) 3x – 4

(D) undefined

**Answer:** 1/3 (x + 4)

17. If f(x) is an odd differentiable function on R, then df(x)/dx is

(A) an even function

(B) an odd function

(C) neither even nor odd function

(D) none of these

**Answer:** an even function

18. Let A = {1,2,3} . Which of the following relations is a function from A to A ?

(A) {(1,1),(2,1),(3,2)}

(B) {(1,1),(1,2)}

(C) {(2,3),(3,1)}

(D) {(1,1),(2,2),(3,3),(1,3),(3,1)}.

**Answer:** {(1,1),(2,1),(3,2)}

19. Let A = {a,b,c} and R = {(a,a),(b,b),(c,c),(b,c),(a,b)} be a relation on A, then R is

(A) symmetric

(B) transitive

(C) reflexive

(D) none of these

**Answer:** reflexive

20. Let ƒ : N → N be defined by the rule f (x) = 2x + 1 for all x ∈ N, then f is

(A) one – one

(B) onto

(C) both one-one and onto

(D) none of these.

**Answer:** one – one