NCERT Class 12 Chapter 1 Maths Relations and Functions MCQ

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1. 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 is congruent to b , a,b∈ T.Then R is

A. equivalence

B. reflexive but not transitive

C. transitive but not symmetric

D. none of these

2. The function f : A → B defined by f(x) = 4x + 7, x ∈ R is

A. one-one

B. Many-one

C. Odd

D. Even

3. 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

4. Let R = { (P,Q) : OP = OQ , O being the origin} be an equivalence relation on A . The equivalence class [( 1,2)] is

CBSE Class12 Maths Relations and Functions (4Q)

A. (A)

B. (B)

C. (C)

D. (D)

5. If a relation R on the set {1,2,3}be defined by R={(1,2)} then R is

A. transitive

B. none of these

C. reflexive

D. symmetric

6. The smallest integer function f(x) = [x] is

A. One-one

B. Many-one

C. Both (a) & (b)

D. None of these

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

A. 1

B. 2

C. 3

D. 4

8. 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)

9. If f: R→ R given by f(x) =(3 − x³)^1/3, find f0f(x)

A. X

B. (3- x³)

C. x³

D. None of these

10. The function f : R → R defined by f(x) = 3 – 4x is

A. Onto

B. Not onto

C. None one-one

D. None of these

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11. The binary operation * defined on N by a * b = a + b + ab for all a, b ∈ N is

A. commutative only

B. associative only

C. both commutative and associative

D. none of these

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

A. 2

B. 3

C. 4

D. None of these

13. The number of bijective functions from set A to itself when A contains 106 elements is

A. 106

B. (106),sup>2

C. 106!

D. 2¹⁰⁶

14. 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

15. Let A = {1, 2, 3, 4} and let R = {(2, 2), (3, 3), (4, 4), (1, 2)} be a relation on A. Then, R is

A. Symmetric

B. Transitive

C. Reflexive

D. Equivalence relation

16. Let f:R→R defined by f(x) = x⁴. Choose the correct answer

A. f is neither one-one nor onto

B. f is oneone but not onto

C. f is many one onto

D. None of these

17. If f(x) = (ax² + b)³, then the function g such that f(g(x)) = g(f(x)) is given by

A. g(x)=(b−x1/3a)

B. g(x)=1(ax2+b)3

C. g(x)=(ax2+b)1/3

D. g(x)=(x1/3−ba)1/2

18. The number of commutative binary operation that can be defined on a set of 2 elements is

A. 8

B. 6

C. 4

D. 2

19. Let f:R→R defined by f(x) = 3x. Choose the correct answer

A. ƒ is one one onto

B. f is many one onto

C. f is one-one but not onto

D. f is neither one-one nor onto

20. If f : R → R, g : R → R and h : R → R is such that f(x) = x², g(x) = tanx and h(x) = logx, then the value of [ho(gof)](x), if x = π√2 will be

A. 0

B. 1

C. -1

D. 10

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21. Set A has 3 elements and the set B has 4 elements. Then the number of injective functions that can be defined from set A to set B is

A. 144

B. 12

C. 24

D. 64

22. If A = {1,3,5,7} and define a relation, such that R =
{ (a,b) a,bA : |a+b| = 8}. Then how many elements are there in the relation R

A. 8

B. 16

C. 1

D. 4

23. If A = {1,2,3}, B = {4,6,9} and R is a relation from A to B defined by ‘ x is smaller than y’. The range of R is

A. {4,6,9}

B. {1}

C. none of these

D. {1, 4,6,9}

24. If f : R → R and g : R → R defined by f(x) = 2x + 3 and g(x) = x² + 7, then the value of x for which f(g(x)) = 25 is

A. ±1

B. ±2

C. ±3

D. ±4

25. Let R be the relation in the set N given by : R = {(a, b): a = b – 2, b > 6}. Then:

A. (2, 4) ∈ R

B. (3, 8) ∈ R

C. (6, 8) ∈ R

D. (8, 7) ∈ R