Class 11 Mathematics Relations and Functions MCQs Set 03

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) = x² + 3x + 5 / x² – 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–x² is:
(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/x³  , 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) = 2^x + 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) n^m – 1
(c) mn – 1
(d) 2^mn – 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 – x² is
(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