Class 11 Mathematics Relations and Functions MCQs Set C

Refer to Class 11 Mathematics Relations and Functions MCQs Set C provided below available for download in Pdf. The MCQ Questions for Class 11 Mathematics with answers are aligned as per the latest syllabus and exam pattern suggested by CBSE, NCERT and KVS. Chapter 2 Relations and Functions Class 11 MCQ are an important part of exams for Class 11 Mathematics and if practiced properly can help you to improve your understanding and get higher marks. Refer to more Chapter-wise MCQs for CBSE Class 11 Mathematics and also download more latest study material for all subjects

MCQ for Class 11 Mathematics Chapter 2 Relations and Functions

Class 11 Mathematics students should refer to the following multiple-choice questions with answers for Chapter 2 Relations and Functions in Class 11.

Chapter 2 Relations and Functions MCQ Questions Class 11 Mathematics with Answers

Question. Which of the following relation is a function ?
(a) {(a, b) (b, e) (c, e) (b, x)}
(b) {(a, d) (a, m) (b, e) (a, b)}
(c) {(a, d) (b, e) (c, d) (e, x)}
(d) {(a, d) (b, m) (b, y) (d, x)}

Answer: C

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

Answer: C

Question. The domain of the function f(x) = x+ 3x + 5 / x– 5x + 4 is
(a) R
(b) R – {1, 4}
(c) R – {1}
(d) (1, 4)

Answer: B

Question. Let X = {1, 2, 3}. The total number of distinct relations that can be defined over X is 2n. The value of ‘n’ is
(a) 9
(b) 6
(c) 8
(d) 2

Answer: A

Question. The domain of f (x) = 1/√2x–1–√1–xis:
(a) 1/2 ,1
(b) [ – 1, ∞]
(c) [1, ∞]
(d) None of the options

Answer: A

Question. The domain and range of the real function f defined by f(x) = |x – 1| is
(a) R, [0, ∞)
(b) R, (–∞, 0)
(c) R, R
(d) (–∞, 0), R

Answer: A

Question. If  f (x) = x3 – 1/x , then f (x) + f (1/x) is equal to
(a) 2 x3
(b) 2.1/x3
(c) 0
(d) 1 

Answer: C

Question. If f(y) = 2y2 + by + c and f(0) = 3 and f(2) = 1, then the value of f(1) is
(a) 0
(b) 1
(c) 2
(d) 3

Answer: A

Question. Let f(x) = 1 + x, g(x) = x2 + x + 1, then (f + g) (x) at x = 0 is
(a) 2
(b) 5
(c) 6
(d) 9

Answer: A

Question. If f (x) = 1– x/1+ x , then f (1– x/1+ x) is equal to:
(a) x
(b) 1– x/1+ x
(c) 1+ x/1– x
(d) 1/x

Answer: A

Question. If f : R → R is defined by f(x) = 3x + |x|, then f(2x) – f (– x) – 6x =
(a) f(x)
(b) 2f(x)
(c) – f(x)
(d) f(– x)

Answer: A

Question. There are three relations R1, R2 and R3 such that
R1 = {(2, 1), (3, 1), (4, 2)},
R2 = {(2, 2), (2, 4), (3, 3), (4, 4)} and
R3 = {(1, 2), (2, 3), (3, 4), (4, 5), (5, 6), (6, 7)}
Then,
(a) R1 and R2 are functions
(b) R2 and R3 are functions
(c) R1 and R3 are functions
(d) Only R1 is a function 

Answer: C

Question. The relation R defined on the set A = {1, 2, 3, 4, 5} by
R = {(x, y) : |x2 – y2| < 16} is given by
(a) {(1, 1), (2, 1), (3, 1), (4, 1), (2, 3)}
(b) {(2, 2), (3, 2), (4, 2), (2, 4)}
(c) {(3, 3), (4, 3), (5, 4), (3, 4)}
(d) None of the options

Answer: D

Question. If n (X) = 5 and n (Y) = 7, then the number of relations on X x Y is 25m. The value of ‘m’ is
(a) 5
(b) 7
(c) 6
(d) 8

Answer: B

Question. If f(x) = 2x + 2–x / 2 , then f(x + y). f(x – y) =
(a) 1/2 [f(2x) + f (2y)]
(b) 1/4 [f (2x) f (2y)]
(c) 1/2[f (2x) – f (2y)]
(d) 1/4[f (2x) – f (2y)]

Answer: A

Question. The cartesian product of A × A has 9 elements, two of which are (–1, 0) and (0, 1), the remaining elements of A × A is given by
(a) {(–1, 1), (0, 0), (–1, –1), (1, –1), (0, –1)}
(b) {(–1, –1), (0, 0), (–1, 1), (1, –1), (1, 0), (1, 1), (0, –1)}
(c) {(1, 0), (0, –1), (0, 0), (–1, –1), (1, –1), (1, 1)}
(d) None of the options

Answer: B

Question. Let A = {x, y, z} and B = {a, b, c, d}. Then, which one of the following is not a relation from A to B?
(a) {(x, a), (x, c)}
(b) {(y, c), (y, d)}
(c) {(z, a), (z, d)}
(d) {(z, b), (y, b), (a, d)}

Answer: D

Question. Let n(A) = m, and n(B) = n. Then the total number of nonempty relations that can be defined from A to B is
(a) mn
(b) nm – 1
(c) mn – 1
(d) 2mn – 1 

Answer: D

Question. If f (x) = x and g (x) = |x|, then (f + g) (x) is equal to
(a) 0 for all x ∈ R
(b) 2x for all x ∈ R
(c) {2x, for x ≥ 0
{0, for x < 0
(d) {0, for x ≥ 0
{2x, for x < 0

Answer: C

Question. A relation R is defined in the set Z of integers as follows (x, y) ∈ R iff x2 + y2 = 9. Which of the following is false?
(a) R = {(0, 3), (0, –3), (3, 0), (–3, 0)}
(b) Domain of R = {–3, 0, 3}
(c) Range of R = {–3, 0, 3}
(d) None of the options

Answer: D

Question. Let set X = {a, b, c} and Y = Φ. The number of ordered pairs in X × Y are
(a) 0
(b) 1
(c) 2
(d) 3

Answer: A

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 the options

Answer: B

Question. If Φ(x) = ax, then [Φ(p)]3 is equal to
(a) Φ (3p)
(b) 3Φ (p)
(c) 6Φ (p)
(d) 2Φ (p)

Answer: A

Question. The domain and range of the relation R given by R = {(x, y) : y = x + 6/x ; where x, y ∈ N and x < 6} is
(a) {1, 2, 3}, {7, 5}
(b) {1, 2}, {7, 5}
(c) {2, 3}, {5}
(d) None of the options

Answer: A

Question. Let N be the set of natural numbers and the relation R be defined such that {R = (x, y) : y = 2x, x, y ∈ N}. Then,
(a) R is a function
(b) R is not a function
(c) domain, range and co-domain is N
(d) None of the above

Answer: A

Question. Suppose that the number of elements in set A is p, the number of elements in set B is q and the number of elements in A × B is 7. Then p2 + q2 =
(a) 42
(b) 49
(c) 50
(d) 51

Answer: C

Question. The domain and range of the function f given by f(x) = 2 – |x – 5| is
(a) Domain = R+, Range = (–∞, 1]
(b) Domain = R, Range = (–∞, 2]
(c) Domain = R, Range = (–∞, 2)
(d) Domain = R+, Range = (–∞, 2]

Answer: B

Question. Let R be the relation on Z defined by
R = {(a, b) : a, b ∈ Z, a – b is an integer}. Then
(a) domain of R is {2, 3, 4, 5, …..}
(b) range of R is Z
(c) Both (a) and (b)
(d) None of the above

Answer: D

Question. If A = {a, b}, B = {c, d}, C = {d, e}, then {(a, c), (a, d), (a, e), (b, c), (b, d), (b, e)} is equal to
(a) A ∩ (B ∪ C)
(b) A ∪ (B ∩ C)
(c) A × (B ∪ C)
(d) A × (B ∩ C)

Answer: C

Question. Let A = {1, 2, 3, 4}, B = {1, 5, 9, 11, 15, 16} and f = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}. Then,
(a) f is a relation from A to B
(b) f is a function from A to B
(c) Both (a) and (b)
(d) None of the options

Answer: A

Question. The domain of the function f(x) = 1/√9 – xis
(a) –3 ≤ x ≤ 3
(b) –3 < x < 3
(c) –9 ≤ x ≤ 9
(d) –9 < x < 9

Answer: B

Statement Type Questions

Question. Consider the following statements.
I. The relation R = {(x, x3) : x is a prime number less than 10 } in Roster form is {(3, 27), (5, 125), (7, 343)}
II. The range of the relation
R = {(x + 2, x + 4) : x ∈ N, x < 8} is {1, 2, 3, 4, 5, 6, 7}.
Choose the correct option.
(a) Only I is true
(b) Only II is true
(c) Both are true
(d) Both are false

Answer: D

Question. Consider the following statements.
I. If the set A has 3 elements and set B = {3, 4, 5}, then the number of elements in A x B = 9.
II. The domain of the relation R defined by
R = {(x, x + 5) : x ∈ (0, 1, 2, 3, 4, 5)} is {5, 6, 7, 8, 9, 10}.
Choose the correct option.
(a) Only I is true.
(b) Only II is true.
(c) Both I and II are true.
(d) Both I and II are false.

Answer: A

Question. Let R be a relation from N to N defined by R = {(a, b) : a, b ∈ N and a = b2}. Then, which of the following is/are true?
I. (a, a) ∈ R for all a ∈ N.
II. (a, b) ∈ R implies (b, a) ∈ R.
III. (a, b) ∈ R, (b, c) ∈ R implies (a, c) ∈ R.
(a) I and II are true
(b) II and III are true
(c) All are true
(d) None of the options

Answer: D

Question. Consider the following statements :
I. If n (A) = p and n (B) = q, then n (A × B) = pq
II. A × Φ = Φ
III. In general, A × B ≠ B × A
Which of the above statements are true ?
(a) Only I
(b) Only II
(c) Only III
(d) All of the above

Answer: D

Question. Which of the following is/are true?
I. If P = {m, n} and Q = {n, m}, then P × Q = {(m, n), (n, m)}.
II. If A and B are non-empty sets, then A × B is a non-empty set of ordered pairs (x, y), such that
x ∈ A and y ∈ B.
III. If A = {1, 2} and B = {3, 4}, then A × (B∩Φ) = Φ.
(a) I and II are true
(b) II and III are true
(c) I and III are true
(d) All are true

Answer: B

Question. Consider the following statements.
I. Let f = {(1, 1), (2, 3), (0, –1), (–1, –3)} be a linear function from Z to Z. Then, f(x) is 2x –1.
II. If f(x) = x3 – 1/x3 , then f(x) + f(1/x) is equal to 0.
Choose the correct option.
(a) Only I is true.
(b) Only II is true.
(c) Both are true.
(d) Both are false.

Answer: C

Question. Consider the following statements.
I. If X = {p, q, r, s} and Y = {1,2, 3, 4, 5}, then {(p, 1), (q, 1), (r, 3), (s, 4)} is a function.
II. 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}.
The relation R in Roster form is {(6, 3), (6, 2), (4, 2)}
Choose the correct option.
(a) Only I is false.
(b) Only II is false.
(c) Both I and II are false.
(d) Neither I nor II is false.

Answer: B

Question. Consider the following statements.
Let A = {1, 2, 3, 4} and B = {5, 7, 9}
I. A x B = B x A
II. n (A x B) = n (B x A)
Choose the correct option.
(a) Statement-I is true.
(b) Statement-II is true.
(c) Both are true.
(d) Both are false.

Answer: B

MCQs for Chapter 2 Relations and Functions Mathematics Class 11

Expert teachers of studiestoday have referred to NCERT book for Class 11 Mathematics to develop the Mathematics Class 11 MCQs. If you download MCQs with answers for the above chapter you will get higher and better marks in Class 11 test and exams in the current year as you will be able to have stronger understanding of all concepts. Daily Multiple Choice Questions practice of Mathematics will help students to have stronger understanding of all concepts and also make them expert on all critical topics. After solving the questions given in the MCQs which have been developed as per latest books also refer to the NCERT solutions for Class 11 Mathematics. We have also provided lot of MCQ questions for Class 11 Mathematics so that you can solve questions relating to all topics given in each chapter. After solving these you should also refer to Class 11 Mathematics MCQ Test for the same chapter.

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