Practice Questions with Answers - Multiple Choice Questions

MCQ Questions for Class 11 Maths Chapter 2 Relations and Functions

MCQ Questions for Class 11 Maths Chapter 2 Relations and Functions

Students are advised to solve the Relations and Functions Multiple Choice Questions of Class 11 Maths to know different concepts. Practicing the MCQ Questions on Relations and Functions Class 11 with answers will boost your confidence thereby helping you score well in the exam.

Explore numerous MCQ Questions of Relations and Functions Class 11 with answers provided with detailed solutions by looking below.

Question 1.
The domain of the function 7-xPx-3 is
(a) {1, 2, 3}
(b) {3, 4, 5, 6}
(c) {3, 4, 5}
(d) {1, 2, 3, 4, 5}

Answer

Answer: (c) {3, 4, 5}
The function f(x) = 7-xPx-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}


Question 2.
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
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 3.
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
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 4.
If the function f : R → R be given by f(x) = x² + 2 and g : R → R is given by g(x) = x/(x – 1). The value of gof(x) is
(a) (x² + 2)/(x² + 1)
(b) x²/(x² + 1)
(c) x²/(x² + 2)
(d) none of these

Answer

Answer: (a) (x² + 2)/(x² + 1)
Given f(x) = x² + 2 and g(x) = x/(x – 1)
Now, gof(x) = g(x² + 2) = (x² + 2)/(x² + 2 – 1) = (x² + 2)/(x² + 1)


Question 5.
Given g(1) = 1 and g(2) = 3. If g(x) is described by the formula g(x) = ax + b, then the value of a and b is
(a) 2, 1
(b) -2, 1
(c) 2, -1
(d) -2, -1

Answer

Answer: (c) 2, -1
Given, g(x) = ax + b
Again, g(1) = 1
⇒ a × 1 + b = 1
⇒ a + b = 1 ……… 1
and g(2) = 3
⇒ a × 2 + b = 3
⇒ 2a + b = 3 …….. 2
Solve equation 1 and 2, we get
a = 2, b = -1


Question 6.
Let f : R → R be a function given by f(x) = x² + 1 then the value of f-1 (26) is
(a) 5
(b) -5
(c) ±5
(d) None of these

Answer

Answer: (c) ±5
Let y = f(x) = x² + 1
⇒ y = x² + 1
⇒ y – 1 = x²
⇒ x = ±√(y – 1)
⇒ f-1 (x) = ±√(x – 1)
Now, f-1 (26) = ±√(26 – 1)
⇒ f-1 (26) = ±√(25)
⇒ f-1 (26) = ±5


Question 7.
the function f(x) = x – [x] has period of
(a) 0
(b) 1
(c) 2
(d) 3

Answer

Answer: (b) 1
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 8.
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
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 9.
The domain of the function f(x) = x/(1 + x²) is
(a) R – {1}
(b) R – {-1}
(c) R
(d) None of these

Answer

Answer: (c) R
Given, function f(x) = x/(1 + x²)
Since f(x) is defined for all real values of x.
So, domain(f) = R


Question 10.
If f : R → R is defined by f(x) = x² – 3x + 2, the f(f(y)) is
(a) x4 + 6x³ + 10x² + 3x
(b) x4 – 6x³ + 10x² + 3x
(c) x4 + 6x³ + 10x² – 3x
(d) x4 – 6x³ + 10x² – 3x

Answer

Answer: (d) x4 – 6x³ + 10x² – 3x
Given, f(x) = x² – 3x + 2
Now, f(f(y)) = f(x² – 3x + 2)
= (x² – 3x + 2)² – 3(x² – 3x + 2) + 2
= x4 – 6x³ + 10x² – 3x