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 - 3
Question 1:
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
Correct Answer – (B)
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 2 :
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
Correct Answer – (A)
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 3 :
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
Correct Answer – (B)
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 4 :
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
Correct Answer – (A)
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 5 :
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.
MCQ Class 11 Mathematics Relations and Functions with Answers
Question 6 :
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}
Correct Answer – (C)
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 7 :
The number of binary operations on the set {a, b} are
(a) 2
(b) 4
(c) 8
(d) 16
Correct Answer – (D)
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 = (nn)²
Given Set = {a, b}
Total number of elements = 2
Total number of binary operations = (2²)² = 24 = 16
Question 8 :
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
Correct Answer – (B)
Given, f(x) = x² and g(x) = 2x + 1
Now gof(x) = g(f(x)) = f(x²) = 2x² + 1
Question 9 :
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 10 :
If f(x) = log3 x and A = (3, 27) then f(A) =
(a) (1, 1)
(b) (3, 3)
(c) (1, 3)
(d) (2, 3)
Correct Answer – (C)
Hint:
Since f(x) = log3 x is an increasing function
So, f(A) = (log3 3, log3 27) = (1, 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
