MCQs For NCERT Class 11 Maths Relations and Functions With Answers

Please refer to the MCQ Questions for Class 11 Relations and Functions Maths Chapter 2 with Answers. The following Relations and Functions Class 11 Mathematics MCQ Questions have been designed based on the latest syllabus and examination pattern for Class 11. Our experts have designed MCQ Questions for Class 11 Relations and Functions with Answers for all chapters in your NCERT Class 11 Mathematics book. You can access all MCQs for Class 11 Mathematics

Relations and Functions Class 11 MCQ Questions with Answers

See below Relations and Functions Class 11 Mathematics MCQ Questions, solve the questions and compare your answers with the solutions provided below.

Question. The domain of definition of the function:   
f(x) = x.1 2(x 4) -0.5 / 2 (x 4)0.5
+ (x + 4)0.5 + 4(x + 4)0.5 is
(a) R
(b) (– 4, 4)
(c) R⁺
(d) (– 4, 0) ∪(0,∞)

Question. The relation R defined on the set of natural numbers as {(a, b) : a differs from b by 3}is given
(a) {(1, 4), (2, 5), (3, 6),…..}
(b) {(4, 1), (5, 2), (6, 3),…..}
(c) {(1, 3), (2, 6), (3, 9),…..}
(d) none of these

Question. The domain of definition of the function   
f (x) = 1 /√x -x
(a) R
(b) (0,∞)
(c) (–∞, 0)
(d) none of these

Question. The range of the function y = 1/2-sin³x for real x is:   
(a) 1/3≤y≤1
(b) -1/3≤y≤1
(c) -1/3≤y>1
d) -1/3>y>1

Question. The domain of the function f (x) = loge(x – [x]) is:   
(a) R
(b) R – Z
(c) (0,+∞)
(d) Z

Question. If P, Q and R are subsets of a set A, then R × (PC È QC)C equals.
(a) (R´ P)Ç(R´Q)
(b) (R´Q)Ç(R´ P)
(c) (R´ P)È(R´Q)
(d) None of these

Question. The domain of the function   
f(x) = 1/√(x¹² – x⁹ +x⁴ -x+1)
(a) (-∞, -1)
(b) (1, ∞)
(c) (-1, 1)
(d) (-∞, ∞)

Question. Range of the function f defined by f (x) [1/sin{x}]   
(where [. ] and {. } respectively denote the greatest integer and the fractional part functions) is
(a) I and set of integers
(b) N, the set of natural numbers
(c) W, the set of whole numbers
(d) {2, 3, 4, …..}

Question. If A × B = { (5, 5), (5, 6), (5, 7), (8, 6), (8, 7), (8, 5)},then the value A.
(a) {5}
(b) {8}
(c) {5, 8}
(d) {5, 6, 7, 8}

Question. Domain of definition of the function   
f x = 3/4-x² + log₁₀ ( x³ -x ) is
(a) (-1, 0)∪(1, 2)∪(2,∞)
(b) (-∞, 2)
(c) (-1, 0) ∪ (0, 2)
(d) (1, 2) ∪ (2, ∞)

Question. If f (x + 1) = x² – 3x + 2, then f (x) is equal to:   
(a) x² – 5x – 6
(b) x² + 5x – 6
(c) x² + 5x + 6
(d) x² – 5x + 6

Question. f (x) = x(x p) /q-p + x(x – q) , p – q.  What is the value of f (p) + f (q) ?   
(a) f (p – q)
(b) f (p + q)
(c) f (p (p + q))
(d) f (q (p – q))

Question. Domain of the function
f (x) =√( 2 – 2x – x²) is :
(a) – √3 ≤ x ≤ + √3
(b) -1- √3 ≤ x ≤ -1+ √3
(c) -2 ≤ x ≤ 2
(d) -2 + √3 ≤ x ≤-2 -√3

Question. If f and g are real functions defined by f(x) = x² + 7 and g (x) = 3x + 5, then f (1/2) × g(14) is
(a) 1336/5
(b) 1363/4
(c) 1251
(d) 1608 

Question. Let A = {1, 2, 3}. The total number of distinct relations that can be defined over A, is
(a) 29
(b) 6
(c) 8
(d) 26 

Question. Let A = {1, 2}, B = {3, 4}. Then, number of subsets of A× B is
(a) 4
(b) 8
(c) 18
(d) 16 

Question. Match the following in column-I with the sets of ordered pairs in column-II. 

Codes:
     A B C D
(a) 1 2 4 3
(b) 3 4 2 1
(c) 3 2 4 1
(d) 1 4 2 3 

Question. If A = {2, 3, 4, 5} and B = {3, 6, 7, 10}. R is a relation defined by R = {(a, b) : a is relatively prime to b, a ∈ A and b ∈ B}, then domain of R is
(a) {2, 3, 5}
(b) {3, 5}
(c) {2, 3, 4}
(d) {2, 3, 4, 5} 

Question. If (4x +3, y) = (3x + 5, – 2), then the sum of the values of x and y is
(a) 0
(b) 2
(c) –2
(d) 1 

Question. The domain for which the functions f(x) = 2x²  – 1 and g(x) = 1 – 3x is equal, i.e. f(x) = g(x), is
(a) {0, 2}
(b) {1/2, – 2}
(c) {–1/2, 2}
(d) {1/2, 2} 

Question. If A = {a, b, c}, B = {b, c, d} and C = {a, d, c}, then (A – B) × (B ∩ C) =
(a) {(a, c), (a, d)}
(b) {(a, b), (c, d)}
(c) {(c, a), (a, d)}
(d) {(a, c), (a, d), (b, d)} 

Question. f (x) = x(x – p)/q – p +  x(x – q)/p – q , p ≠ q. What is the value of f (p) + f (q) ?
(a) f (p – q)
(b) f (p + q)
(c) f (p (p + q))
(d) f (q (p – q)) 

Question. If A = {3, 4} and B = {5, 6, 7}. Then match the column-I with the column-II. 

Codes:
     A B C
(a) 1 2 3
(b) 1 3 2
(c) 2 3 1
(d) 3 2 1 

ASSERTION – REASON TYPE QUESTIONS

(a) Assertion is correct, Reason is correct; Reason is a correct explanation for assertion.
(b) Assertion is correct, Reason is correct; Reason is not a correct explanation for Assertion
(c) Assertion is correct, Reason is incorrect
(d) Assertion is incorrect, Reason is correct. 

Question. Assertion : Let f and g be two real functions given by
f = {(0, 1), (2, 0), (3, –4), (4, 2), (5, 1)} and
g = {(1, 0), (2, 2), (3, –1), (4, 4), (5, 3)}
Then, domain of f · g is given by {2, 3, 4, 5}.
Reason : Let f and g be two real functions. Then, (f · g) (x) = f {g(x)}. 

Question. Let A = {1, 2, 3, 4, 6}. If R is the relation on A defined by {(a, b) : a, b ∈ A, b is exactly divisible by a}.
Assertion : The relation R in Roster form is {(6, 3), (6, 2), (4, 2)}.
Reason : The domain and range of R is {1, 2, 3, 4, 6}. 

Question. Assertion : If A = {x, y, z} and B = {3, 4}, then number of relations from A to B is 2⁵.
Reason : Number of relations from A to B is 2^{n(A) × n(B)}. 

Question. Let A = {a, b, c, d, e, f, g, h} and R = {(a, a), (b, b), (a, g), (b, a), (b, g), (g, a), (g, b), (g, g), (b, b)}
Consider the following statements:
Assertion : R ⊂ A × A.
Reason : R is not a relation on A. 

Question. Assertion : If (x + 1, y – 2) = (3, 1), then x = 2 and y = 3.
Reason : Two ordered pairs are equal, if their corresponding elements are equal. 

Question. Assertion : If f(x) = 1/x – 2,x ≠ 2 and g(x) = (x – 2)², then 
(f + g) (x) = 1+ (x – 2)³ / x – 2 , x ≠ 2.
Reason : If f and g are two functions, then their sum is defined by (f + g) (x) = f(x) + g(x)  x ∈ D₁ ∩ D₂, where D₁ and D₂ are domains of f and g, respectively.