These Relations And Functions Class 12 MCQ And Answers are most important for your upcoming examinations including JEE Main & JEE Advanced. These Relations And Functions Class 12 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 Class 12 MCQ And Answers

1. A relation R in human being defined as, R = {{a, b) : a, b ∈ human beings: a loves A} is-

(A) reflexive

(B) symmetric and transitive

(C) equivalence

(D) None of these

**Answer:** equivalence

2. If A = (1, 2, 3}, B = {6, 7, 8} is a function such that f(x) = x + 5 then what type of a function is f?

(A) Many-one onto

(B) Constant function

(C) one-one onto

(D) into

**Answer:** one-one onto

3. If the function f(x) = x³ + ex/2 and g (x) = fn(x), then the value of g'(1) is

(A) 1

(B) 2

(C) 3

(D) 4

**Answer:** 2

4. If A = [1, 2, 3}, B = {5, 6, 7} and f: A → B is a function such that f(x) = x + 4 then what type of function is f?

(A) into

(B) one-one onto

(C) many-onto

(D) constant function

**Answer:** one-one onto

5. 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

**Answer:** transitive

6. Let A = {1, 2,3,…. n} and B = { a, b}. Then the number of surjections from A into B is

(A) ^{nP}_{2}

(B) 2n – 2

(C) 2n – 1

(D) None of these

**Answer:** 2n – 2

7. Let f: R → R be the function 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

**Answer:** (x -5)^{1/3}

8. 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

**Answer:** 31

9. If f(x_{1}) = f (x_{2}) ⇒ x_{1} = x_{2} ∀ x_{1} x_{2} ∈ A then the function f: A → B is

(A) many one

(B) one-one onto

(C) onto

(D) one-one

**Answer:** one-one

10. What type of relation is ‘less than’ in the set of real numbers?

(A) only symmetric

(B) only transitive

(C) only reflexive

(D) equivalence

**Answer:** only transitive

11. 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

**Answer:** 14

12. Let R be a relation on the set N of natural numbers denoted by nRm ⇔ n is a factor of m (i.e. n | m). Then, R is

(A) Reflexive and symmetric

(B) Transitive and symmetric

(C) Equivalence

(D) Reflexive, transitive but not symmetric

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

13. The relation R is defined on the set of natural numbers as {(a, b): a = 2b}. Then, R^{-1} is given by

(A) {(2, 1), (4, 2), (6, 3),….}

(B) {(1, 2), (2, 4), (3, 6),….}

(C) R^{-1} is not defined

(D) None of these

**Answer:** {(1, 2), (2, 4), (3, 6),….}

15. Let P = {(x, y) | x² + y² = 1, x, y ∈ R]. Then, P is

(A) Reflexive

(B) Symmetric

(C) Transitive

(D) Anti-symmetric

**Answer:** Symmetric

16. Let R be a relation on the set N be defined by {(x, y) | x, y ∈ N, 2x + y = 41}. Then R is

(A) Reflexive

(B) Symmetric

(C) Transitive

(D) None of these

**Answer:** None of these

17. If f(x) + 2f (1 – x) = x² + 2 ∀ x ∈ R, then f(x) =

(A) x² – 2

(B) 1

(C) 1/3 (x – 2)²

(D) None of these

**Answer:** 1/3 (x – 2)²

19. The domain of sin-1 (log (x/3)] is. .

(A) [1, 9]

(B) [-1, 9]

(C) [-9, 1]

(D) [-9, -1]

**Answer:** [1, 9]

20. 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 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

**Answer:** equivalence