**Find here the NCERT chapter-wise Multiple Choice Questions from Class 12 Mathematics book Chapter 1 Relations and Functions with Answers Pdf free download. This may assist you to understand and check your knowledge about the chapters. Students also can take a free test of the Multiple Choice Questions of Relations and Functions. Each question has four options followed by the right answer. These MCQ Questions are selected supported by the newest exam pattern as announced by CBSE.**

## NCERT MCQ Chapters for Class 12 Mathematics

## Q1. The function f : R → R defined by f(x) = 3 – 4x is

(i) Onto

(ii) Not onto

(iii) None one-one

(iv) None of these

(i) Onto

## Q2. Given set A = {a, b, c). An identity relation in set A is

(i) R = {(a, b), (a, c)}

(ii) R = {(a, a), (b, b), (c, c)}

(iii) R = {(a, a), (b, b), (c, c), (a, c)}

(iv) R= {(c, a), (b, a), (a, a)}

(ii) R = {(a, a), (b, b), (c, c)}

## Q3. If an operation is defined by a* b = a² + b², then (1 * 2) * 6 is

(i) 12

(ii) 28

(iii) 61

(iv) None of these

(iii) 61

## Q4. Let f : R → R be defined as f(x) = 3x. Then

(i) f is one-one onto

(ii) f is many-one onto

(iii) f is one-one but not onto

(iv) f is neither one-one nor onto.

(i) f is one-one onto

## Q5. The smallest integer function f(x) = [x] is

(i) One-one

(ii) Many-one

(iii) Both (i) & (ii)

(iv) None of these

(ii) Many-one

## Q6. Given set A ={1, 2, 3} and a relation R = {(1, 2), (2, 1)}, the relation R will be

(i) reflexive if (1, 1) is added

(ii) symmetric if (2, 3) is added

(iii) transitive if (1, 1) is added

(iv) symmetric if (3, 2) is added

(iii) transitive if (1, 1) is added

## Q7. 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}

(i) Reflexive

(ii) Transitive

(iii) Symmetric

(iv) None of these

(iv) None of these

## Q8. Let A = (1, 2, 3). Then the number of equivalence relations containing (1, 2) is

(i) 1

(ii) 2

(iii) 3

(iv) 4.

(ii) 2

## Q9. The function f : A → B defined by f(x) = 4x + 7, x ∈ R is

(i) one-one

(ii) Many-one

(iii) Odd

(iv) Even

(i) one-one

## Q10. Let R be a relation on the set L of lines defined by l1 R l2 if l1 is perpendicular to l2, then relation R is

(i) reflexive and symmetric

(ii) symmetric and transitive

(iii) equivalence relation

(iv) symmetric

(iv) symmetric

## Q11. Consider the binary operation * on a defined by x * y = 1 + 12x + xy, ∀ x, y ∈ Q, then 2 * 3 equals

(i) 31

(ii) 40

(iii) 43

(iv) None of these

(i) 31

## Q12. Let A = {1, 2, 3}. Then number of relations containing {1, 2} and {1, 3}, which are reflexive and symmetric but not transitive is:

(i) 1

(ii) 2

(iii) 3

(iv) 4.

(i) 1

## Q13. 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

(i) ±1

(ii) ±2

(iii) ±3

(iv) ±4

(ii) ±2

## Q14. A relation S in the set of real numbers is defined as xSy ⇒ x – y+ √3 is an irrational number, then relation S is

(i) reflexive

(ii) reflexive and symmetric

(iii) transitive

(iv) symmetric and transitive

(i) reflexive

## Q15. Let R be a relation on the set N of natural numbers defined by nRm if n divides m. Then R is

(i) Reflexive and symmetric

(ii) Transitive and symmetric

(iii) Equivalence

(iv) Reflexive, transitive but not symmetric.

(ii) Transitive and symmetric

## Q16. If f : R → R, g : R → R and h : R → R are such that f(x) = x², g(x) = tan x and h(x) = log x, then the value of (go(foh)) (x), if x = 1 will be

(i) 0

(ii) 1

(iii) -1

(iv) π

(i) 0

## Q17. 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

(i) 144

(ii) 12

(iii) 24

(iv) 64

(iii) 24

## Q18. Let f: R → R be defined by f(x) = sin x and g : R → R be defined by g(x) = x², then fog is

(i) x² sin x

(ii) (sin x)²

(iii) sin x²

(iv) sin/x2

(iii) sin x²

## Q19. The number of binary operations that can be defined on a set of 2 elements is

(i) 8

(ii) 4

(iii) 16

(iv) 64

(iii) 16

## Q20. If A, B and C are three sets such that A ∩ B = A ∩ C and A ∪ B = A ∪ C. then

(i) A = B

(ii) A = C

(iii) B = C

(iv) A ∩ B = d

(iii) B = C

## Q21. Let f: R → R be defined by f(x) = x² + 1. Then pre-images of 17 and – 3 respectively, are

(i) ø, {4,-4}

(ii) {3, -3}, ø

(iii) {4, -4}, ø

(iv) {4, -4}, {2,-2}.

(iii) {4, -4}, $

## Q22. Let * be a binary operation on set Q – {1} defind by a * b = a + b – ab : a, b ∈ Q – {1}. Then * is

(i) Commutative

(ii) Associative

(iii) Both (i) and (ii)

(iv) None of these

(iii) Both (i) and (ii)

## Q23. Let A = {1, 2}, how many binary operations can be defined on this set?

(i) 8

(ii) 10

(iii) 16

(iv) 20

(iii) 16

## Q24. The maximum number of equivalence relations on the set A = {1, 2, 3} are

(i) 1

(ii) 2

(iii) 3

(iv) 5

(iv) 5

## Q25. Let the function ‘f’ be defined by f (x) = 5x² + 2 ∀ x ∈ R, then ‘f’ is

(i) onto function

(ii) one-one, onto function

(iii) one-one, into function

(iv) many-one into function

(iv) many-one into function

## Q26. Let R be the relation “is congruent to” on the set of all triangles in a plane is

(i) reflexive

(ii) symmetric

(iii) symmetric and reflexive

(iv) equivalence

(iv) equivalence

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