Relations and Functions Class 12 MCQ-16 to 30

Question 16.
A relation R in human being defined as, R = {{a, b) : a, b ∈ human beings : a loves A} is-
(a) reflexive
(b) symmetric and transitive
(c) equivalence
(d) None of these

Answer

Answer: (c) equivalence

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Question 17.
If f(x) + 2f (1 – x) = x² + 2 ∀ x ∈ R, then f(x) =
(a) x² – 2
(b) 1
(c) \(\frac{1}{3}\) (x – 2)²
(d) None of these

Answer

Answer: (c) \(\frac{1}{3}\) (x – 2)²

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Question 18.
The period of sin² θ is
(a) π²
(b) π
(c) 2π
(d) \(\frac{π}{2}\)

Answer

Answer: (b) π

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Question 19.
The domain of sin-1 (log (x/3)] is. .
(a) [1, 9]
(b) [-1, 9]
(c) [-9, 1]
(d) [-9, -1]

Answer

Answer: (a) [1, 9]

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Question 20.
f(x) = \(\frac{log_2(x+3)}{x^2+3x+2}\) is the domain of
(a) R – {-1, -2}
(b) (- 2, ∞) .
(c) R- {- 1,-2, -3}
(d) (-3, + ∞) – {-1, -2}

Answer

Answer: (d) (-3, + ∞) – {-1, -2}

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Question 21.
If the function f(x) = x³ + e^x/2 and g (x) = fⁿ(x), then the value of g'(1) is
(a) 1
(b) 2
(c) 3
(d) 4

Answer

Answer: (b) 2

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Question 22.
What type of relation is ‘less than’ in the set of real numbers?
(a) only symmetric
(b) only transitive
(c) only reflexive
(d) equivalence

Answer

Answer: (b) only transitive

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Question 23.
If A = [1, 2, 3}, B = {5, 6, 7} and f: A → B is a function such that f(x) = x + 4 then what type of function is f?
(a) into
(b) one-one onto
(c) many-onto
(d) constant function

Answer

Answer: (b) one-one onto

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Question 24.
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

Answer: (a) range (f) ⊂ B

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Question 25.
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

Answer: (c) one-one into

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Question 26.
If f: R → R such that f(x) = 3x – 4 then which of the following is f^-1(x)?
(a) \(\frac{1}{3}\) (x + 4)
(b) \(\frac{1}{3}\) (x – 4)
(c) 3x – 4
(d) undefined

Answer

Answer: (a) \(\frac{1}{3}\) (x + 4)

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Question 27.
A = {1, 2, 3} which of the following function f: A → A does not have an inverse function
(a) {(1, 1), (2, 2), (3, 3)}
(b) {(1, 2), (2, 1), (3, 1)}
(c) {(1, 3), (3, 2), (2, 1)}
(d) {(1, 2), (2, 3), (3, 1)

Answer

Answer: (b) {(1, 2), (2, 1), (3, 1)}

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Question 28.
Let T be the set of all triangles in the Euclidean plane, and let a relation R on T be defined as aRb if a congruent to b ∀ a, b ∈ T. Then R is
(a) reflexive but-not transitive
(b) transitive but not symmetric
(c) equivalence
(d) None of these

Answer

Answer: (c) equivalence

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Question 29.
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

Answer: (b) transitive but not symmetric

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Question 30.
The maximum number of equivalence relations on the set A = {1, 2, 3} are
(a) 1
(b) 2
(c) 3
(d) 5

Answer

Answer: (d) 5

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