MCQs for Class 12 Maths Chapter 1 Relations and Functions

Check the below NCERT MCQ Questions for Class 12 Maths Chapter 1 Relations and Functions with Answers Pdf free download. MCQ Questions for Class 12 Maths with Answers were prepared based on the latest exam pattern. We have provided Relations and Functions Class 12 Maths MCQs Questions with Answers to help students understand the concept very well.

Relations and Functions Class 12 MCQs Questions with Answers

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 oneAnswer

Answer: (a) one-one

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 theseAnswer

Answer: (d) None of these

Question 3.
If F : R → R such that f(x) = 5x + 4 then which of the following is equal to f^-1(x).
(a)x−54

(b)

(c)

(d)

-5x−45

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 theseAnswer

Answer: (c) 61

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 theseAnswer

Answer: (a) 31(x−1)(3−x)Answer

Answer: (a) [1, 3]

Question 7.
If f: R → R defined by f(x) = 2x + 3 then f^-1(x) =
(a) 2x – 3
(b)x−32

(c)

(d) None of thesex2Answer

Answer: (a) even function

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) 8Answer

Answer: (a) 14

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 = dAnswer

Answer: (c) B = C

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

Answer: (c) 16

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

n

(d) nAnswer

Answer: (c) [n

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) intoAnswer

Answer: (c) one-one onto

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) (1+x2

)^1/3

Answer: (d) (

)^1/3

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 functionAnswer

Answer: (d) many-one into function

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 theseAnswer

Answer: (c) equivalence

Question 17.
If f(x) + 2f (1 – x) = x² + 2 ∀ x ∈ R, then f(x) =
(a) x² – 2
(b) 1
(c)13

(x – 2)²
(d) None of theseAnswerπ2Answer

Answer: (b) π

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]

Question 20.
f(x) =+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}

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) 4Answer

Answer: (b) 2

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) equivalenceAnswer

Answer: (b) only transitive

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 functionAnswer

Answer: (b) one-one onto

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) ⊂ AAnswer

Answer: (a) range (f) ⊂ B

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 intoAnswer

Answer: (c) one-one into

Question 26.
If f: R → R such that f(x) = 3x – 4 then which of the following is f^-1(x)?
(a)13

(x + 4)
(b)

(x – 4)
(c) 3x – 4
(d) undefinedAnswer

Answer: (a)

(x + 4)

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)}

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