Check the below NCERT MCQ Questions for Class 11 Maths Chapter 2 Relations and Functions with Answers Pdf free download. MCQ Questions for Class 11 Maths with Answers were prepared based on the latest exam pattern. We have provided Relations and Functions Class 11 Maths MCQs Questions with Answers to help students understand the concept very well.

## Relations and Functions Class 11 MCQs Questions with Answers

Question 1.

If f(x) = (a – x)^{1/n}, a > 0 and n ∈ N, then the value of f(f(x)) is

(a) 1/x

(b) x

(c) x²

(d) x^{1/2}

## Answer

Answer: (b) x

Hint:

Given, f(x) = (a – x)^{1/n}

Now, f(f(x)) = [(a – f(x))^{n}]^{1/n}

⇒ f(f(x)) = [(a – {(a – x^{n})^{1/n} }^{n} ]^{1/n}

⇒ f(f(x)) = [a – (a – x^{n})]^{1/n}

⇒ f(f(x)) = [a – a + x^{n})]^{1/n}

⇒ f(f(x)) = (x^{n})^{1/n}

⇒ f(f(x)) = x

Question 2.

The domain of the definition of the real function f(x) = √(log_{12} x² ) of the real variable x is

(a) x > 0

(b) |x| ≥ 1

(c) |x| > 4

(d) x ≥ 4

## Answer

Answer: (b) |x| ≥ 1

Hint:

We have f(x) = √(log_{12} x²)

Since, log_{a} k ≥ 0 if a > 1, k ≥ 1

or 0 < a < 1 and 0 < k ≤ 1

So, the function f(x) exists if

log_{12} x² ≥ 0

⇒ x² ≥ 1

⇒ |x| ≥ 1

Question 3.

If f(x) = e^{x} and g(x) = log_{e} x then the value of fog(1) is

(a) 0

(b) 1

(c) -1

(d) None of these

## Answer

Answer: (b) 1

Hint:

Given, f(x) = e^{x}

and g(x) = log x

fog(x) = f(g(x))

= f (log x)

= e^{log x}

= x

So, fog(1) = 1

Question 4.

Two functions f and g are said to be equal if f

(a) the domain of f = the domain of g

(b) the co-domain of f = the co-domain of g

(c) f(x) = g(x) for all x

(d) all of above

## Answer

Answer: (d) all of above

Hint:

Two functions f and g are said to be equal if f

1. the domain of f = the domain of g

2. the co-domain of f = the co-domain of g

3. f(x) = g(x) for all x

Question 5.

A function f(x) is said to be an odd function if

(a) f(-x) = f(x)

(b) f(-x) = -f(x)

(c) f(-x) = k * f(x) where k is a constant

(d) None of these

## Answer

Answer: (b) f(-x) = -f(x)

Hint:

A function f(x) is said to be an odd function if

f(-x) = -f(x) for all x

Question 6.

If f(x) is an odd differentiable function on R, then df(x)/dx is a/an

(a) Even function

(b) Odd function

(c) Either even or odd function

(d) Neither even nor odd function

## Answer

Answer: (a) Even function

Hint:

Given, f(x) is an odd differentiable function on R

⇒ f(-x) = -f(x) for all x ∈ R

differentiate on both side, we get

⇒ -df(-x)/dx = -df(x)/dx for all x ∈ R

⇒ df(-x)/dx = df(x)/dx for all x ∈ R

⇒ df(x)/dx is an even function on R.

Question 7.

The function f(x) = sin (πx/2) + cos (πx/2) is periodic with period

(a) 4

(b) 6

(c) 12

(d) 24

## Answer

Answer: (a) 4

Hint:

Period of sin (πx/2) = 2π/(π/2) = 4

Period of cos (πx/2) = 2π/(π/2) = 4

So, period of f(x) = LCM (4, 4) = 4

Question 8.

If f(x) = log_{3} x and A = (3, 27) then f(A) =

(a) (1, 1)

(b) (3, 3)

(c) (1, 3)

(d) (2, 3)

## Answer

Answer: (c) (1, 3)

Hint:

Since f(x) = log_{3} x is an increasing function

So, f(A) = (log_{3} 3, log_{3} 27) = (1, 3)

Question 9.

The domain of tan^{-1} (2x + 1) is

(a) R

(b) R -{1/2}

(c) R -{-1/2}

(d) None of these

## Answer

Answer: (a) R

Hint:

Since tan^{-1} x exists if x ∈ (-∞, ∞)

So, tan^{-1} (2x + 1) is defined if

-∞ < 2x + 1 < ∞

⇒ -∞ < x < ∞

⇒ x ∈ (-∞, ∞)

⇒ x ∈ R

So, domain of tan^{-1} (2x + 1) is R.

Question 10.

the function f(x) = x – [x] has period of

(a) 0

(b) 1

(c) 2

(d) 3

## Answer

Answer: (b) 1

Hint:

Let T is a positive real number.

Let f(x) is periodic with period T.

Now, f(x + T) = f(x), for all x ∈ R

⇒ x + T – [x + T] = x – [x], for all x ∈ R

⇒ [x + T] – [x] = T, for all x ∈ R

Thus, there exist T > 0 such that f(x + T) = f(x) for all x ∈ R

Now, the smallest value of T satisfying f(x + T) = f(x) for all x ∈ R is 1

So, f(x) = x – [x] has period 1

Question 11.

If f(x) =(3x – 2)/(2x – 3) then the value of f(f(x)) is

(a) x

(b) x²

(c) x³

(d) None of these

## Answer

Answer: (a) x

Hint:

Given, f(x) = (3x – 2)/(2x – 3)

Now, f(f(x)) = f{(3x – 2)/(2x – 3)}

= {(3×(3x – 2)/(2x – 3) – 2)}/{(2(3x – 2)/(2x – 3) – 3)}

= {(9x – 6)/(2x – 3) – 2)}/{((6x – 4)/(2x – 3) – 3)}

= [{(9x – 6) – 2(2x – 3)}/(2x – 3)]/[{(6x – 4) – 3(2x – 3)}/(2x – 3)]

= {(9x – 6) – 2(2x – 3)}/{(6x – 4) – 3(2x – 3)}

= (9x – 6 – 4x + 6)/(6x – 4 – 6x + 9)

= 5x/5

= x

So, f(f(x)) = x

Question 12.

Let R be the set of real numbers. If f(x) = x² and g(x) = 2x + 1, then fog(x) is equal to

(a) 2x + 1

(b) 2x² + 1

(c) (2x + 1)²

(d) None of these

## Answer

Answer: (b) 2x² + 1

Hint:

Given, f(x) = x² and g(x) = 2x + 1

Now gof(x) = g(f(x)) = f(x²) = 2x² + 1

Question 13.

A relation R is defined from the set of integers to the set of real numbers as (x, y) = R if x² + y² = 16 then the domain of R is

(a) (0, 4, 4)

(b) (0, -4, 4)

(c) (0, -4, -4)

(d) None of these

## Answer

Answer: (b) (0, -4, 4)

Hint:

Given that:

(x, y) ∈ R ⇔ x² + y² = 16

⇔ y = ±√(16 – x² )

when x = 0 ⇒ y = ±4

(0, 4) ∈ R and (0, -4) ∈ R

when x = ±4 ⇒ y = 0

(4, 0) ∈ R and (-4, 0) ∈ R

Now for other integral values of x, y is not an integer.

Hence R = {(0, 4), (0, -4), (4, 0), (-4, 0)}

So, Domain(R) = {0, -4, 4}

Question 14.

The number of binary operations on the set {a, b} are

(a) 2

(b) 4

(c) 8

(d) 16

## Answer

Answer: (d) 16

Hint:

Let S is a finite set containing n elements.

Since binary operation on S is a function from S×S to S, therefore total number of

binary operations on S is the

total number of functions from S×S to S = (n^{n})²

Given Set = {a, b}

Total number of elements = 2

Total number of binary operations = (2²)² = 2^{4} = 16

Question 15.

If f is an even function and g is an odd function the fog is a/an

(a) Even function

(b) Odd function

(c) Either even or odd function

(d) Neither even nor odd function

## Answer

Answer: (a) Even function

Hint:

Given, f is an even function and g is an odd function.

Now, fog(-x) = f{g(-x)}

= f{-g(x)} {since g is an odd function}

= f{g(x)} for all x {since f is an even function}

So, fog is an even function.

Question 16.

The domain of the function f(x) = 1/(x² – 3x + 2) is

(a) {1, 2}

(b) R

(c) R – {1, 2}

(d) R – {1, -2}

## Answer

Answer: (c) R – {1, 2}

Hint:

Given, function is f(x) = 1/(x² – 3x + 2)

Clearly, f(x) is not defined when x² – 3x + 2 = 0

⇒ (x – 1)×(x – 1) = 0

⇒ x = 1, 2

So, f(x) is not defined when x = 1, 2

So, domain of function is R – {1, 2}

Question 17.

The domain of the function f(x) = sin^{-1} (tan x) is

(a) -π/4 ≤ x ≤ π/4

(b) nπ – π/4 ≤ x ≤ nπ + π/4

(c) nπ – π/3 ≤ x ≤ nπ + π/3

(d) -π/3 ≤ x ≤ π/3

## Answer

Answer: (b) nπ – π/4 ≤ x ≤ nπ + π/4

Hint:

sin^{-1} (tan x) is defined for -1 ≤ tan x ≤ 1

= -π/4 ≤ x ≤ π/4

The general solution of the above inequality is

nπ -π/4 ≤ x ≤ nπ + π/4

Question 18.

Let A = {-2, -1, 0} and f(x) = 2x – 3 then the range of f is

(a) {7, -5, -3}

(b) {-7, 5, -3}

(c) {-7, -5, 3}

(d) {-7, -5, -3}

## Answer

Answer: (d) {-7, -5, -3}

Hint:

Given, A = {-2, -1, 0}

and f(x) = 2x – 3

Now, f(-2) = 2 × (-2) – 3 = -4 – 3 = -7

f(-1) = 2 × (-1) – 3 = -2 – 3 = -5

f(0) = 2 × 0 – 3 = -3

So, range of f = {-7, -5, -3}

Question 19.

The range of the function ^{7-x}P_{x-3} is

(a) {1, 2, 3, 4, 5}

(b) {3, 4, 5}

(c) None of these

(d) {1, 2, 3}

## Answer

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

Hint:

The function f(x) = ^{7-x}P_{x-3} is defined only if x is an integer satisfying the following inequalities:

1. 7 – x ≥ 0

2. x – 3 ≥ 0

3. 7 – x ≥ x – 3

Now, from 1, we get x ≤ 7 ……… 4

from 2, we get x ≥ 3 ……………. 5

and from 2, we get x ≤ 5 ………. 6

From 4, 5 and 6, we get

3 ≤ x ≤ 5

So, the domain is {3, 4, 5}

Now, f(3) = ^{7-3}P_{3-3} = ^{4}P_{0} = 1

⇒ f(4) = ^{7-4}P_{4-3} = ^{3}P_{1} = 3

⇒ f(5) = ^{7-5}P_{5-3} = ^{2}P_{2} = 2

So, the range of the function is {1, 2, 3}

Question 20.

The period of the function f(x) = sin^{4} 3x + cos^{4} 3x is

(a) π/2

(b) π/3

(c) π/4

(d) π/6

## Answer

Answer: (d) π/6

Hint:

Since g(x) = sin^{4} x + cos^{4} x is periodic with period π/2

So, f(x) = sin^{4} 3x + cos^{4} 3x is periodic with period (π/2)/3 = π/6

We hope the given NCERT MCQ Questions for Class 11 Maths Chapter 2 Relations and Functions with Answers Pdf free download will help you. If you have any queries regarding CBSE Class 11 Maths Relations and Functions MCQs Multiple Choice Questions with Answers, drop a comment below and we will get back to you soon.

## Leave a Reply