Relations and Functions  MCQs

MCQs of Relations and Functions

Showing 61 to 70 out of 98 Questions
4 5 6 7 8 9
61.
If f : R → R, f(x) = [ x ], then f -1 _____.
(a) does not exist
(b) = f
(c) x
(d) = ⌈ x ⌉
Answer:

Option (a)

62.
If f : R → Z, f(x) = ⌈ x ⌉, then f -1does not exist, because_____.
(a) f is not one - one, f is not onto
(b) f is one - one, f is not onto
(c) f is not one - one, f is onto
(d) f is one - one, f is onto
Answer:

Option (c)

63.
For f : A → B, ∃ a function g : B → A  such that gof = IA, then _____.
(a) f is onto
(b) f is not onto
(c) f is one - one
(d) f is not one - one
Answer:

Option (c)

64.
The relation S = {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5)} on A = {1, 2, 3, 4, 5} is _____.
(a) symmetric only
(b) reflexive only
(c) transitive only
(d) an equivalence relation
Answer:

Option (d)

65.
Which of the following defined on Z is not an equivalence relation ?
(a) (x, y) ∈ S ⇔ x ≥ y
(b) (x, y) ∈ S ⇔ x = y
(c) (x, y) ∈ S ⇔ x - y is a multiple of 3
(d) (x, y) ∈ S ⇔x - y even
Answer:

Option (a)

66.
f: -π2, π2 → -1, 1 is a bijection, if _____.
(a) f(x) = x
(b) f(x) = sinx
(c) f(x) = x2
(d) f(x) = cosx
Answer:

Option (b)

67.
f : (-1, 1) →R, f(x) =x1 - x, then f-1(x)  = _____.
(a) 1x2 + 1
(b) - signum xxx1 - x
(c) -x1 - x
(d) x2x2 + 1
Answer:

Option (d)

68.
If f : R → R, f(x)= x2, g : R → R, g(x)= 2x, then { x | (fog) (x) = (gof) (x) } = _____.
(a) {0}
(b) {0, 1}
(c) R
(d) {0, 2}
Answer:

Option (d)

69.
f : R → R, f(x) = 2x + 2x  is _____.
(a) one - one and onto
(b) one - one but not onto
(c) many - one and onto
(d) many - one but not onto
Answer:

Option (b)

70.
If f : R → R, f(x) = ⌈ x ⌉, g : R → R, g(x) = cos x, h : R → R, h(x) = 3x, then ho (gof) = _____.
(a) cos ⌈ x ⌉
(b) ⌈cos 3x ⌉
(c) 3cos ⌈ x ⌉
(d) cos 3 ⌈ x ⌉
Answer:

Option (c)

Showing 61 to 70 out of 98 Questions
4 5 6 7 8 9