These Relations And Functions NCERT Questions And Answers are most important for your upcoming examinations including JEE Main & JEE Advanced. These Relations And Functions NCERT Questions 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 NCERT Questions And Answers

1. Let A = {1,2,3} and B = {2,3,4}, then which of the following is a funtion from A to B?

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

(B) {(1,3),(2,4)}

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

(D) {(1,2),(2,3),(3,4),(3,2)}

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

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

(A) 0

(B) 1

(C) 2

(D) More than 2

**Answer:** 2

3. let A = {1,2,3} . Which of the following functions on A is invertible ?

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

(B) f = {(1,2),(2,3),(3,1)}

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

(D) f = {(1,1),(2,2),(3,1)}

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

4. Let f (x) = x^{2} and g (x) = √x , then

(A) (gof) (x) = |x| for all x ∈ R

(B) (fog) (x) = x^{2} for all x ∈ R

(C) (fog) (x) = (gof) (x) for all x ∈ R

(D) none of these

**Answer:** (gof) (x) = |x| for all x ∈ R

5. If log_{12} 27 = a then the value of log_{6} 16 is

(A) (3 – a)/{(3 + a)

(B) 2*(3 – a)/{(3 + a)

(C) 3*(3 – a)/{(3 + a)

(D) 4*(3 – a)/{(3 + a)

**Answer:** 4*(3 – a)/{(3 + a)

6. The range of the function f(x) = |x – 3| is

(A) R

(B) (0, ∞)

(C) (-∞, 0)

(D) None of these

**Answer:** (0, ∞)

7. A = {1, 2, 3} which of the following function f: A → A does not have an inverse function

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

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

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

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

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

8. 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, ∞)

**Answer:** [1, ∞)

9. Let f: A → B and g : B → C be the bijective functions. Then (g o f)^{-1} is,

(A) f^{-1} o g^{-1}

(B) f o g

(C) g^{-1} o f^{-1}

(D) g o f

**Answer:** f^{-1} o g^{-1}

10. Which one of the following relations on R is an equivalence relation?

(A) aR_{1}b ⇔ |a| = |b|

(B) aR_{2}b ⇔ a ≥ b

(C) aR_{3}b ⇔ a divides b

(D) aR_{4}b ⇔ a < b

**Answer:** aR_{1}b ⇔ |a| = |b|

11. If A, B and C are three sets such that A ∩ B = A ∩ C and A ∪ B = A ∪ C. then

(A) A = B

(B) A = C

(C) B = C

(D) A ∩ B = d

**Answer:** B = C

12. If an operation is defined by a* b = a² + b², then (1 * 2) * 6 is

(A) 12

(B) 28

(C) 61

(D) None of these

**Answer:** 61

13. The period of sin² θ is

(A) π²

(B) π

(C) 2π

(D) π/2

**Answer:** π

14. Let the function ‘f’ be defined by f (x) = 5x² + 2 ∀ x ∈ R, then ‘f’ is

(A) onto function

(B) one-one, onto function

(C) one-one, into function

(D) many-one into function

**Answer:** many-one into function

15. Let A = {1, 2}, how many binary operations can be defined on this set?

(A) 8

(B) 10

(C) 16

(D) 20

**Answer:** 16