Relations and Functions Class 12 MCQ-01 to 15

 

Question 1.
If f(x₁) = f (x₂) ⇒ x₁ = x₂ ∀ x₁ x₂ ∈ A then the function f: A → B is
(a) one-one
(b) one-one onto
(c) onto
(d) many one

Answer

Answer: (a) one-one

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Question 2.
What type of a relation is R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} on the set A – {1, 2, 3, 4}
(a) Reflexive
(b) Transitive
(c) Symmetric
(d) None of these

Answer

Answer: (d) None of these

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Question 3.
If F : R → R such that f(x) = 5x + 4 then which of the following is equal to f^-1(x).
(a) \(\frac{x-5}{4}\)
(b) \(\frac{x-y}{5}\)
(c) \(\frac{x-4}{5}\)
(d) \(\frac{x}{4}\) -5

Answer

Answer: (c) \(\frac{x-4}{5}\)

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Question 4.
If an operation is defined by a* b = a² + b², then (1 * 2) * 6 is
(a) 12
(b) 28
(c) 61
(d) None of these

Answer

Answer: (c) 61

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Question 5.
Consider the binary operation * on a defined by x * y = 1 + 12x + xy, ∀ x, y ∈ Q, then 2 * 3 equals
(a) 31
(b) 40
(c) 43
(d) None of these

Answer

Answer: (a) 31

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Question 6.
The range of the function f(x) = \(\sqrt{(x-1)(3-x)}\) is
(a) [1, 3]
(b) [0, 1]
(c) [-2, 2]
(d) None of these

Answer

Answer: (a) [1, 3]

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Question 7.
If f: R → R defined by f(x) = 2x + 3 then f^-1(x) =
(a) 2x – 3
(b) \(\frac{x-3}{2}\)
(c) \(\frac{x+3}{2}\)
(d) None of these

Answer

Answer: (b) \(\frac{x-3}{2}\)

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Question 8.
The function f(x) = log (x² + \(\sqrt{x^2+1}\) ) is
(a) even function
(b) odd function
(c) Both
(d) None of these

Answer

Answer: (a) even function

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Question 9.
Let E = {1, 2, 3, 4} and F = {1, 2} Then, the number of onto functions from E to F is
(a) 14
(b) 16
(c) 12
(d) 8

Answer

Answer: (a) 14

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Question 10.
If A, B and C are three sets such that A ∩ B = A ∩ C and A ∪ B = A ∪ C. then
(a) A = B
(b) A = C
(c) B = C
(d) A ∩ B = d

Answer

Answer: (c) B = C

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Question 11.
Let A = {1, 2}, how many binary operations can be defined on this set?
(a) 8
(b) 10
(c) 16
(d) 20

Answer

Answer: (c) 16

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Question 12.
Let A = {1, 2, 3, 4,…. n} How many bijective function f : A → B can be defined?
(a) \(\frac{1}{2}\)n

(d) n

Answer

Answer: (c) [n

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Question 13.
If A = (1, 2, 3}, B = {6, 7, 8} is a function such that f(x) = x + 5 then what type of a function is f?
(a) Many-one onto
(b) Constant function
(c) one-one onto
(d) into

Answer

Answer: (c) one-one onto

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Question 14.
Let function R → R is defined as f(x) = 2x³ – 1, then ‘f’ is
(a) 2x³ + 1
(b) (2x)³ + 1
(c) (1 – 2x)³
(d) (\(\frac{1+x}{2}\))^1/3

Answer

Answer: (d) (\(\frac{1+x}{2}\))^1/3

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Question 15.
Let the functioin ‘f’ be defined by f (x) = 5x² + 2 ∀ x ∈ R, then ‘f’ is
(a) onto function
(b) one-one, onto function
(c) one-one, into function
(d) many-one into function

Answer

Answer: (d) many-one into function

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