CBSE Class 11 Mathematics Chapter 2 Relations and Functions Multiple Choice Questions with Answers. MCQ Class 11 Mathematics Relations and Functions with Answers was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 11 Mathematics Relations and Functions MCQs with Answers to know their preparation level.
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MCQ Class 11 Mathematics Relations and Functions with Answers - Set - 4
Question 1:
the function f(x) = x – [x] has period of
(a) 0
(b) 1
(c) 2
(d) 3
Correct Answer – (B)
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 2 :
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
Correct Answer – (C)
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 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
Correct Answer – (D)
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 :
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}
Correct Answer – (C)
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 5 :
The range of the function 7-xPx-3 is
(a) {1, 2, 3, 4, 5}
(b) {3, 4, 5}
(c) None of these
(d) {1, 2, 3}
Correct Answer – (D)
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}
Now, f(3) = 7-3P3-3 = 4P0 = 1
⇒ f(4) = 7-4P4-3 = 3P1 = 3
⇒ f(5) = 7-5P5-3 = 2P2 = 2
So, the range of the function is {1, 2, 3}
MCQ Class 11 Mathematics Relations and Functions with Answers
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
Correct Answer – (C)
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 :
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
Correct 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 8 :
The domain of tan-1 (2x + 1) is
(a) R
(b) R – {1/2}
(c) R – {-1/2}
(d) None of these
Correct Answer – (A)
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 9 :
The period of the function f(x) = sin4 3x + cos4 3x is
(a) π/2
(b) π/3
(c) π/4
(d) π/6
Correct Answer – (D)
Since g(x) = sin4 x + cos4 x is periodic with period π/2
So, f(x) = sin4 3x + cos4 3x is periodic with period (π/2)/3 = π/6
Question 10 :
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}
Correct Answer – (D)
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}
- NCERT Solutions Class 11 Mathematics Relations and Functions : Exercise 2.1
- NCERT Solutions Class 11 Mathematics Relations and Functions : Exercise 2.2
- NCERT Solutions Class 11 Mathematics Relations and Functions : Exercise 2.3
- NCERT Solutions Class 11 Mathematics Relations and Functions : Exercise 2 Misc
- NCERT Solutions Class 11 Mathematics Textbook download
