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NCERT Solutions for class 12 Maths | Chapter 1 - Relations and Functions

(1) Consider the non-empty set consisting of children is a family and a relation R defined as aRb If a is brother of b. Then R is
[A] symmetric but not transitive
[B] transitive but not symmetric
[C] neither symmetric nor transitive
[D] both symmetric and transitive
Answer: transitive but not symmetric
(2) Let A = {1, 2, 3} and consider the relation R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)}. Then R is
[A] reflexive but not symmetric
[B] reflexive-but not transitive.
[C] symmetric and transitive
[D] neither symmetric, nor transitive
Answer: reflexive but not symmetric

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(3) Let f: [0, 1| → [0, 1| be defined by

[A] Constant
[B] 1 + x
[C] x
[D] None of these
Answer: X
(4) If f: R → R defined by f(x) = 2x + 3 then f-1(x) =
[A] 2x – 3
[B] x-3/2
[C] x+3/2
[D] None of these
Answer: x-3/2
(5) f(x) = is the domain of
[A] R – {-1, -2}
[B] (- 2, ∞) .
[C] R- {- 1,-2, -3}
[D] (-3, + ∞) – {-1, -2}
Answer: (-3, + ∞) – {-1, -2}
(6) f: A → B will be an into function if
[A] range (f) ⊂ B
[B] f(a) = B
[C] B ⊂ f(a)
[D] f(b) ⊂ A
Answer: range (f) ⊂ B
(7) If f : R → R such that f(x) = 3x then what type of a function is f?
[A] one-one onto
[B] many one onto
[C] one-one into
[D] many-one into
Answer: one-one into
(8) The maximum number of equivalence relations on the set A = {1, 2, 3} are
[A] 1
[B] 2
[C] 3
[D] 5
Answer: 5
(9) Let f: N → R be the function defined by f(x) = 2x−1/2 and g: Q → R be another function defined by g (x) = x + 2. Then (g 0 f) 3/2 is
[A] 1
[B] 0
[C] 7/2
[D] None of these
Answer: None of these
(10) If f: R → R such that f(x) = 3x – 4 then which of the following is f-1(x)?
[A] 1/3 (x + 4)
[B] 1/3 (x – 4)
[C] 3x – 4
[D] undefined
Answer: 1/3 (x + 4)
(11) If f(x) is an odd differentiable function on R, then df(x)/dx is
[A] an even function
[B] an odd function
[C] neither even nor odd function
[D] none of these
Answer: an even function
(12) Let A = {1,2,3} . Which of the following relations is a function from A to A ?
[A] {(1,1),(2,1),(3,2)}
[B] {(1,1),(1,2)}
[C] {(2,3),(3,1)}
[D] {(1,1),(2,2),(3,3),(1,3),(3,1)}.
Answer: {(1,1),(2,1),(3,2)}
(13) Let A = {a,b,c} and R = {(a,a),(b,b),(c,c),(b,c),(a,b)} be a relation on A, then R is
[A] symmetric
[B] transitive
[C] reflexive
[D] none of these
Answer: reflexive
(14) Let ƒ : N → N be defined by the rule f (x) = 2x + 1 for all x ∈ N, then f is
[A] one - one
[B] onto
[C] both one-one and onto
[D] none of these .
Answer: one - one
(15) Let A = {1,2,3} and B = {2,3,4}, then which of the following is a funtion from A to B ?
[A] {(1,2),(1,3),(2,3)(3,3)}
[B] {(1,3),(2,4)}
[C] {(1,3),(2,3),(3,3)}
[D] {(1,2),(2,3),(3,4),(3,2)}
Answer: {(1,3),(2,3),(3,3)}
(16) Let A = {1, 2, 3}. Then number of equivalence relations containing (1, 2) is
[A] 0
[B] 1
[C] 2
[D] More than 2
Answer: 2
(17) let A = {1,2,3} . Which of the following functions on A is invertible ?
[A] f = {(1,1),(2,1),(3,1)}
[B] f = {(1,2),(2,3),(3,1)}
[C] f = {(1,1),(2,3),(3,2)}
[D] f = {(1,1),(2,2),(3,1)}
Answer: f = {(1,2),(2,3),(3,1)}
(18) Let f (x) = x2 and g (x) = √x , then
[A] (gof) (x) = |x| for all x ∈ R
[B] (fog) (x) = x2 for all x ∈ R
[C] (fog) (x) = (gof) (x) for all x ∈ R
[D] none of these
Answer: (gof) (x) = |x| for all x ∈ R
(19) If log12 27 = a then the value of log6 16 is
[A] (3 - a)/{(3 + a)
[B] 2*(3 - a)/{(3 + a)
[C] 3*(3 - a)/{(3 + a)
[D] 4*(3 - a)/{(3 + a)
Answer: 4*(3 - a)/{(3 + a)
(20) The range of the function f(x) = |x - 3| is
[A] R
[B] (0, ∞)
[C] (-∞, 0)
[D] None of these
Answer: (0, ∞)

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