MCQ Questions for Class 12 Maths Chapter 1 Relations and Functions with Answers

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Relations and Functions Class 12 MCQs Questions with Answers

Don’t forget to practice the multitude of MCQ Questions on Relations and Functions Class 12 with answers so you can apply your skills during the exam.

Question 1.
Let R be the relation in the set (1, 2, 3, 4}, given by:
R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}.
Then:
(a) R is reflexive and symmetric but not transitive
(b) R is reflexive and transitive but not symmetric
(c) R is symmetric and transitive but not reflexive
(d) R is an equivalence relation.

Answer: (b) R is reflexive and transitive but not symmetric

Question 2.
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.

Answer: (c) (6, 8) ∈ R

Question 3.
Let A = {1, 2, 3}. Then number of relations containing {1, 2} and {1, 3}, which are reflexive and symmetric but not transitive is:
(a) 1
(b) 2
(c) 3
(d) 4.

Question 4.
Let A = (1, 2, 3). Then the number of equivalence relations containing (1, 2) is
(a) 1
(b) 2
(c) 3
(d) 4.

Question 5.
Let f: R → R be defined as f(x) = x4. Then
(a) f 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.

Answer: (d) f is neither one-one nor onto.

Question 6.
Let f : R → R be defined as f(x) = 3x. Then
(a) f 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.

Answer: (a) f is one-one onto

Question 7.
If f: R → R be given by f(x) = (3 – x³)1/3, then fof (x) is
(a) x1/3
(b) x³
(c) x
(d) 3 – x³.

Question 8.
Let f: R – {-$$\frac { 4 }{3}$$} → R be a function defined as: f(x) = $$\frac { 4x }{3x+4}$$, x ≠ –$$\frac { 4 }{3}$$. The inverse of f is map g : Range f → R -{-$$\frac { 4 }{3}$$} given by
(a) g(y) = $$\frac { 3y }{3-4y}$$
(b) g(y) = $$\frac { 4y }{4-3y}$$
(c) g(y) = $$\frac { 4y }{3-4y}$$
(d) g(y) = $$\frac { 3y }{4-3y}$$

Answer: (b) g(y) = $$\frac { 4y }{4-3y}$$

Question 9.
Let R be a relation on the set N of natural numbers defined by nRm if n divides m. Then R is
(a) Reflexive and symmetric
(b) Transitive and symmetric
(c) Equivalence
(d) Reflexive, transitive but not symmetric.

Question 10.
Set A has 3 elements and the set B has 4 elements. Then the number of injective mappings that can be defined from A to B is:
(a) 144
(b) 12
(c) 24
(d) 64

Question 11.
Let f: R → R be defined by f(x) = sin x and g : R → R be defined by g(x) = x², then fog is
(a) x² sin x
(b) (sin x)²
(c) sin x²
(d) $$\frac { sin x }{x^2}$$

Question 12.
Let f: R → R be defined by f(x) = x² + 1. Then pre-images of 17 and – 3 respectively, are
(a) ø, {4,-4}
(b) {3, -3}, ø
(c) {4, -4}, ø
(d) {4, -4}, {2,-2}.

Question 13.
Let f: R → R be defined by
f(x)= $$\left\{\begin{array}{lr} 2 x ; & x>3 \\ x^{2} ; & 1<x<3 \\ 3 x ; & x \leq 1 \end{array}\right.$$
(a) 9
(b) 14
(c) 5
(d) None of these.

Question 14.
The domain of the function f (x) = $$\frac { 1 }{\sqrt{|x|-x}}$$ is
(a) (-∞, ∞)
(b) (0, ∞)
(c) (-∞, 0)
(d) (-∞, ∞) – {0}.

Hint:
f(x) = $$\frac { 1 }{\sqrt{|x|-x}}$$
f(x) is defined if |x| – x > 0
if |x| > x
if x < 0.
Hence, Df = (-∞, 0).

Question 15.
If a ∈ R and the equation
-3(x – [x] )2 + 2 (x – [x]) + a² = 0,
where [x] denotes the greatest integer (≤ x) has no integral solution, then all possible values of a lie in the interval:
(a) (1, 2)
(b) (-2, -1)
(c) (-∞, -2) ∪(2, ∞)
(d) (-1, 0) ∪ (0, 1).

Answer: (d) (-1, 0) ∪ (0, 1).
Hint:
Put x – [x] = t.
Then – 3t² + 2t + a² = 0
⇒ a² = 3t² – 2t.
For non-integral solutions, 0 < a² < 1.
Hence, as (- 1, 0) ∪ (0, 1).

Fill in the Blanks

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

Question 2.
If A = {0, 1, 3}, then the number of relations on A is ………………..

Question 3.
A bijective function is both ……………….. and ………………

Question 4.
Let R be a relation defined on A = { 1, 2, 3) by R = {(1, 3), (3, 1), (2, 2)}, R is ………………..

Question 5.
If f be the greatest integer function defined as f(x) = [x] and g be the modulus function defined as g(x) = |x|, then the value of gof ($$\frac { -5 }{4}$$) is ………………..

Hint:
gof ($$\frac { -5 }{4}$$) = g (f($$\frac { -5 }{4}$$))
= g(-2) = |-2| = 2.

Question 6.
If f : R → R is defined by 3x + 4, then f(f(x)) is …………….

Hint:
f(f (x)) = f(3x + 4)
= 3f(x) + 4
= 3 (3x + 4) + 4
= 9x + 16.

Question 7.
If f(x) = ex and g(x) = log x, then gof is ……………….

Hint:
gof (x) = g(f(x) = g (ex)
= log ex = x log e = x(1) = x.

Question 8.
The domain of the function f (x) = $$\frac { x }{|x|}$$ is ………………..

Hint:
f is defined for all x ∈ R except at x = 0.

Question 9.
Let f: R – {-$$\frac { 4 }{3}$$} → R be a function defined as: f(x) = $$\frac { 4x }{3x+4}$$, x ≠ –$$\frac { 4 }{3}$$
Then inverse of f is map g : Range f → R – {-$$\frac { 4 }{3}$$} given by …………………

Answer: g(y) = $$\frac { 4x }{3x+4}$$
Let y = f(x)= $$\frac { 4x }{3x+4}$$
⇒ x = $$\frac { 4y }{4-3y}$$