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(x_{1}) = f (x_{2}) ⇒ x_{1} = x_{2} ∀ x_{1} x_{2} ∈ 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

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

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) \(\frac{x-4}{5}\)

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

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

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]

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) \(\frac{x-3}{2}\)

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

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

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

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

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

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

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}

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

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

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

Question 18.

The period of sin² θ is

(a) π²

(b) π

(c) 2π

(d) \(\frac{π}{2}\)

## Answer

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) = \(\frac{log_2(x+3)}{x^2+3x+2}\) 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}

Question 21.

If the function f(x) = x³ + e^{x/2} and g (x) = f^{n}(x), then the value of g'(1) is

(a) 1

(b) 2

(c) 3

(d) 4

## Answer

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) equivalence

## Answer

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 function

## Answer

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) ⊂ A

## Answer

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 into

## Answer

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) \(\frac{1}{3}\) (x + 4)

(b) \(\frac{1}{3}\) (x – 4)

(c) 3x – 4

(d) undefined

## Answer

Answer: (a) \(\frac{1}{3}\) (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

(d) None of these

## Answer

Answer: (c) equivalence

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

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

Question 31.

If a relation R on the set {1, 2, 3} be defined by R = {(1, 2)}, then R is

(a) reflexive

(b) transitive

(c) symmetric

(d) None of these

## Answer

Answer: (b) transitive

Question 32.

Let us define a relation R in R as aRb if a ≥ b. Then R is

(a) an equivalence relation

(b) reflexive, transitive but not symmetric

(c) neither transitive nor reflexive but symmetric

(d) symmetric, transitive but not reflexive

## Answer

Answer: (b) reflexive, transitive but not symmetric

Question 33.

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

Answer: (a) reflexive but not symmetric

Question 34.

The identity element for the binary operation * defined on Q ~ {0} as

a * b = \(\frac{ab}{2}\) ∀ a, b ∈ Q ~ {0} is

(a) 1

(b) 0

(c) 2

(d) None of these

## Answer

Answer: (c) 2

Question 35.

If the set A contains 5 elements and the set B contains 6 elements, then the number of one-one and onto mappings from A to B is

(a) 720

(b) 120

(c) 0

(d) None of these

## Answer

Answer: (c) 0

Question 36.

Let A = {1, 2,3,…. n} and B = { a, b}. Then the number of surjections from A into B is

(a) ^{n}P_{2}

(b) 2^{n} – 2

(c) 2^{n} – 1

(d) None of these

## Answer

Answer: (b) 2^{n} – 2

Question 37.

Let f : R → R be defined by f (x) = \(\frac{1}{x}\) ∀ x ∈ R. Then f is

(a) one-one

(b) onto

(c) bijective

(d) f is not defined

## Answer

Answer: (d) f is not defined

Question 38.

Let f: R → R. be defined by f (x) = 3x² – 5 and g : R → R by g (x) = \(\frac{x}{x^2+1}\). Then g o f is

## Answer

Answer: (a)

Question 39.

Which of the following functions from Z into Z are bijective?

(a) f(x) = x³

(b) f(x) = x + 2

(c) f(x) = 2x + 1

(d) f{x) = x² + 1

## Answer

Answer: (b) f(x) = x + 2

Question 40.

Let f: R → R be the function defined by f(x) = x³ + 5. Then f^{-1} (x) is

(a) (x + 5)^{1/3}

(b) (x -5)^{1/3}

(c) (5 – x)^{1/3}

(d) 5 – x

## Answer

Answer: (b) (x -5)^{1/3}

Question 41.

Let f: A → B and g : B → C be the bijective functions. Then (g o f)^{-1} is,

(a) f^{-1} o g^{-1}

(b) f o g

(c ) g^{-1} o f^{-1}

(d) g o f

## Answer

Answer: (a) f^{-1} o g^{-1}

Question 42.

Let f: R – {\(\frac{3}{5}\)} → R be defined by f(x) = \(\frac{3x+2}{5x-3}\) then

(a) f^{-1}(x) = f(x)

(b) f^{-1}(x) = -f(x)

(c ) (f o f)x = -x

(d ) f^{-1}(x) = \(\frac{1}{19}\) f(x)

## Answer

Answer: (a) f^{-1}(x) = f(x)

Question 43.

Let f: [0, 1| → [0, 1| be defined by

(a) Constant

(b) 1 + x

(c) x

(d) None of these

## Answer

Answer: (c) x

Question 44.

Let f: |2, ∞) → R be the function defined by f(x) – x² – 4x + 5, then the range of f is

(a) R

(b) [1, ∞)

(c) [4, ∞)

(d) [5, ∞)

## Answer

Answer: (b) [1, ∞)

Question 45.

Let f: N → R be the function defined by f(x) = \(\frac{2x-1}{2}\) and g: Q → R be another function defined by g (x) = x + 2. Then (g 0 f) \(\frac{3}{2}\) is

(a) 1

(b) 0

(c) \(\frac{7}{2}\)

(d) None of these

## Answer

Answer: (d) None of these

Question 46.

Let f: R → R be defined by

then f(- 1) + f (2) + f (4) is

(a) 9

(b) 14

(c) 5

(d) None of these

## Answer

Answer: (a) 9

Question 47.

Let f : R → R be given by f (,v) = tan x. Then f^{-1}(1) is

(a) \(\frac{π}{4}\)

(b) {nπ + \(\frac{π}{4}\) : n ∈ Z}

(c) does not exist

(d) None of these

## Answer

Answer: (b) {nπ + \(\frac{π}{4}\) : n ∈ Z}

Question 48.

The relation R is defined on the set of natural numbers as {(a, b): a = 2b}. Then, R^{-1} is given by

(a) {(2, 1), (4, 2), (6, 3),….}

(b) {(1, 2), (2, 4), (3, 6),….}

(c) R^{-1} is not defined

(d) None of these

## Answer

Answer: (b) {(1, 2), (2, 4), (3, 6),….}

Question 49.

The relation R = {(1,1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)} on set A = {1, 2, 3} is

(a) Reflexive but not symmetric

(b) Reflexive but not transitive

(c) Symmetric and transitive

(d) Neither symmetric nor transitive

## Answer

Answer: (a) Reflexive but not symmetric

Question 50.

Let P = {(x, y) | x² + y² = 1, x, y ∈ R]. Then, P is

(a) Reflexive

(b) Symmetric

(c) Transitive

(d) Anti-symmetric

## Answer

Answer: (b) Symmetric

Question 51.

Let R be an equivalence relation on a finite set A having n elements. Then, the number of ordered pairs in R is

(a) Less than n

(b) Greater than or equal to n

(c) Less than or equal to n

(d) None of these

## Answer

Answer: (b) Greater than or equal to n

Question 52.

For real numbers x and y, we write xRy ⇔ x – y + √2 is an irrational number. Then, the relational R is

(a) Reflexive

(b) Symmetric

(c) Transitive

(d) None of these

## Answer

Answer: (a) Reflexive

Question 53.

Let R be a relation on the set N be defined by {(x, y) | x, y ∈ N, 2x + y = 41}. Then R is

(a) Reflexive

(b) Symmetric

(c) Transitive

(d) None of these

## Answer

Answer: (d) None of these

Question 54.

Which one of the following relations on R is an equivalence relation?

(a) aR_{1}b ⇔ |a| = |b|

(b) aR_{2}b ⇔ a ≥ b

(c) aR_{3}b ⇔ a divides b

(d) aR_{4}b ⇔ a < b

## Answer

Answer: (a) aR_{1}b ⇔ |a| = |b|

Question 55.

Let R be a relation on the set N of natural numbers denoted by nRm ⇔ n is a factor of m (i.e. n | m). Then, R is

(a) Reflexive and symmetric

(b) Transitive and symmetric

(c) Equivalence

(d) Reflexive, transitive but not symmetric

## Answer

Answer: (d) Reflexive, transitive but not symmetric

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