## Relations and Functions Class 12 Maths MCQs Pdf

**Relation And Function Class 12 MCQ Question 1.**

The function f : A → B defined by f(x) = 4x + 7, x ∈ R is

(a) one-one

(b) Many-one

(c) Odd

(d) Even

Answer:

(a) one-one

**Relations And Functions Class 12 MCQ Question 2.**

The smallest integer function f(x) = [x] is

(a) One-one

(b) Many-one

(c) Both (a) & (b)

(d) None of these

Answer:

(b) Many-one

**MCQ On Relation And Function Class 12 Question 3.**

The function f : R → R defined by f(x) = 3 – 4x is

(a) Onto

(b) Not onto

(c) None one-one

(d) None of these

Answer:

(a) Onto

**MCQ Of Relation And Function Class 12 Question 4.**

The number of bijective functions from set A to itself when A contains 106 elements is

(a) 106

(b) (106)^{2}

(c) 106!

(d) 2^{106}

Answer:

(c) 106!

**Relation And Function Class 12 MCQ Questions Question 5.**

If f(x) = (ax^{2} + b)^{3}, then the function g such that f(g(x)) = g(f(x)) is given by

(a) g(x)=(b−x1/3a)

(b) g(x)=1(ax2+b)3

(c) g(x)=(ax2+b)1/3

(d) g(x)=(x1/3−ba)1/2

Answer:

(d) g(x)=(x1/3−ba)1/2

**Relation And Function MCQ Question 6.**

If f : R → R, g : R → R and h : R → R is such that f(x) = x^{2}, g(x) = tanx and h(x) = logx, then the value of [ho(gof)](x), if x = π√2 will be

(a) 0

(b) 1

(c) -1

(d) 10

Answer:

(a) 0

**MCQ Of Maths Class 12 Chapter 1 Question 7.**

If f : R → R and g : R → R defined by f(x) = 2x + 3 and g(x) = x^{2} + 7, then the value of x for which f(g(x)) = 25 is

(a) ±1

(b) ±2

(c) ±3

(d) ±4

Answer:

(b) ±2

**Class 12 Maths Chapter 1 MCQ Questions Question 8.**

Let f : N → R : f(x) = (2x−1)2 and g : Q → R : g(x) = x + 2 be two functions. Then, (gof) (32) is

(a) 3

(b) 1

(c) 72

(d) None of these

Answer:

(a) 3

**Relation And Function MCQ Class 12 Question 9.**

Let f(x)=x−1x+1, then f(f(x)) is

(a) 1x

(b) −1x

(c) 1x+1

(d) 1x−1

Answer:

(b) −1x

**Class 12 Maths Chapter 1 MCQ Question 10.**

If f(x) = 1−1x, then f(f(1x))

(a) 1x

(b) 11+x

(c) xx−1

(d) 1x−1

Answer:

(c) xx−1

**MCQs On Relations And Functions Class 12 Question 11.**

If f : R → R, g : R → R and h : R → R are such that f(x) = x^{2}, g(x) = tan x and h(x) = log x, then the value of (go(foh)) (x), if x = 1 will be

(a) 0

(b) 1

(c) -1

(d) π

Answer:

(a) 0

**MCQ Relation And Function Class 12 Question 12.**

If f(x) = 3x+25x−3 then (fof)(x) is

(a) x

(b) -x

(c) f(x)

(d) -f(x)

Answer:

(a) x

**Class 12 Maths Ch 1 MCQ Questions Question 13.**

If the binary operation * is defind on the set Q+ of all positive rational numbers by a * b = ab4. Then, 3∗(15∗12) is equal to

(a) 3160

(b) 5160

(c) 310

(d) 340

Answer:

(a) 3160

**Relation Function Class 12 MCQ Question 14.**

The number of binary operations that can be defined on a set of 2 elements is

(a) 8

(b) 4

(c) 16

(d) 64

Answer:

(c) 16

**Relations And Functions MCQ Question 15.**

Let * be a binary operation on Q, defined by a * b = 3ab5 is

(a) Commutative

(b) Associative

(c) Both (a) and (b)

(d) None of these

Answer:

(c) Both (a) and (b)

**MCQ Questions On Relations And Functions Class 12 Question 16.**

Let * be a binary operation on set Q of rational numbers defined as a * b = ab5. Write the identity for *.

(a) 5

(b) 3

(c) 1

(d) 6

Answer:

(a) 5

**MCQ On Relations And Functions Pdf Question 17.**

For binary operation * defind on R – {1} such that a * b = ab+1 is

(a) not associative

(b) not commutative

(c) commutative

(d) both (a) and (b)

Answer:

(d) both (a) and (b)

**Class 12 Maths MCQ Chapter 1 Question 18.**

The binary operation * defind on set R, given by a * b = a+b2 for all a,b ∈ R is

(a) commutative

(b) associative

(c) Both (a) and (b)

(d) None of these

Answer:

(a) commutative

**Class 12 Relation And Function MCQ Question 19.**

Let A = N × N and * be the binary operation on A defined by (a, b) * (c, d) = (a + c, b + d). Then * is

(a) commutative

(b) associative

(c) Both (a) and (b)

(d) None of these

Answer:

(c) Both (a) and (b)

**Relation And Function Class 12 MCQ Questions Pdf Question 20.**

Find the identity element in the set I^{+} of all positive integers defined by a * b = a + b for all a, b ∈ I^{+}.

(a) 1

(b) 2

(c) 3

(d) 0

Answer:

(d) 0

Question 21.

Let * be a binary operation on set Q – {1} defind by a * b = a + b – ab : a, b ∈ Q – {1}. Then * is

(a) Commutative

(b) Associative

(c) Both (a) and (b)

(d) None of these

Answer:

(c) Both (a) and (b)

Question 22.

The binary operation * defined on N by a * b = a + b + ab for all a, b ∈ N is

(a) commutative only

(b) associative only

(c) both commutative and associative

(d) none of these

Answer:

(c) both commutative and associative

Question 23.

The number of commutative binary operation that can be defined on a set of 2 elements is

(a) 8

(b) 6

(c) 4

(d) 2

Answer:

(d) 2

Question 24.

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 is 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:

(c) equivalence

Question 25.

The maximum number of equivalence relations on the set A = {1, 2, 3} are

(a) 1

(b) 2

(c) 3

(d) 5

Answer:

(d) 5

Question 26.

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) symmetric, transitive but not reflexive

(d) neither transitive nor reflexive but symmetric

Answer:

(b) reflexive, transitive but not symmetric

Question 27.

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:

(a) reflexive but not symmetric

Question 28.

The identity element for the binary operation * defined on Q – {0} as a * b = ab2 ∀ a, b ∈ Q – {0) is

(a) 1

(b) 0

(c) 2

(d) None of these

Answer:

(c) 2

Question 29.

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

(a) nP2

(b) 2^{n} – 2

(c) 2^{n} – 1

(d) none of these

Answer:

(b) 2^{n} – 2

Question 30.

Let f : R → R be defind by f(x) = 1x ∀ x ∈ R. Then f is

(a) one-one

(b) onto

(c) bijective

(d) f is not defined

Answer:

(d) f is not defined

Question 31.

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

(a) f(x) = x^{3}

(b) f(x) = x + 2

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

(d) f(x) = x^{2} + 1

Answer:

(b) f(x) = x + 2

Question 32.

Let f : R → R be the functions defined by f(x) = x^{3} + 5. Then f^{-1}(x) is

(a) (x+5)13

(b) (x−5)13

(c) (5−x)13

(d) 5 – x

Answer:

(b) (x−5)13

Question 33.

Let f : R – {35} → R be defined by f(x) = 3x+25x−3. Then

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

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

(c) (fof) x = -x

(d) f^{-1}(x) = 119 f(x)

Answer:

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

Question 34.

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

(a) π4

(b) {nπ + π4; n ∈ Z}

(c) Does not exist

(d) None of these

Answer:

(b) {nπ + π4; n ∈ Z}

Question 35.

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:

(d) Reflexive, transitive but not symmetric

Question 36.

Let S = {1, 2, 3, 4, 5} and let A = S × S. Define the relation R on A as follows:

(a, b) R (c, d) iff ad = cb. Then, R is

(a) reflexive only

(b) Symmetric only

(c) Transitive only

(d) Equivalence relation

Answer:

(d) Equivalence relation

Question 37.

Let R be the relation “is congruent to” on the set of all triangles in a plane is

(a) reflexive

(b) symmetric

(c) symmetric and reflexive

(d) equivalence

Answer:

(d) equivalence

Question 38.

Total number of equivalence relations defined in the set S = {a, b, c} is

(a) 5

(b) 3!

(c) 23

(d) 33

Answer:

(a) 5

Question 39.

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 defiend

(d) None of these

Answer:

(b) {(1, 2), (2, 4), (3, 6), ……..}

Question 40.

Let X = {-1, 0, 1}, Y = {0, 2} and a function f : X → Y defiend by y = 2x^{4}, is

(a) one-one onto

(b) one-one into

(c) many-one onto

(d) many-one into

Answer:

(c) many-one onto

Question 41.

Let f : R → R be a function defined by f(x)=e|x|−e−xex+e−x then f(x) is

(a) one-one onto

(b) one-one but not onto

(c) onto but not one-one

(d) None of these

Answer:

(d) None of these

Question 42.

Let g(x) = x^{2} – 4x – 5, then

(a) g is one-one on R

(b) g is not one-one on R

(c) g is bijective on R

(d) None of these

Answer:

(b) g is not one-one on R

Question 43.

Let A = R – {3}, B = R – {1}. Let f : A → B be defined by f(x)=x−2x−3. Then,

(a) f is bijective

(b) f is one-one but not onto

(c) f is onto but not one-one

(d) None of these

Answer:

(a) f is bijective

Question 44.

The mapping f : N → N is given by f(n) = 1 + n^{2}, n ∈ N when N is the set of natural numbers is

(a) one-one and onto

(b) onto but not one-one

(c) one-one but not onto

(d) neither one-one nor onto

Answer:

(c) one-one but not onto

Question 45.

The function f : R → R given by f(x) = x^{3} – 1 is

(a) a one-one function

(b) an onto function

(c) a bijection

(d) neither one-one nor onto

Answer:

(c) a bijection

Question 46.

Let f : [0, ∞) → [0, 2] be defined by f(x)=2×1+x, then f is

(a) one-one but not onto

(b) onto but not one-one

(c) both one-one and onto

(d) neither one-one nor onto

Answer:

(a) one-one but not onto

Question 47.

If N be the set of all-natural numbers, consider f : N → N such that f(x) = 2x, ∀ x ∈ N, then f is

(a) one-one onto

(b) one-one into

(c) many-one onto

(d) None of these

Answer:

(b) one-one into

Question 48.

Let A = {x : -1 ≤ x ≤ 1} and f : A → A is a function defined by f(x) = x |x| then f is

(a) a bijection

(b) injection but not surjection

(c) surjection but not injection

(d) neither injection nor surjection

Answer:

(a) a bijection

Question 49.

Let f : R → R be a function defined by f(x) = x^{3} + 4, then f is

(a) injective

(b) surjective

(c) bijective

(d) none of these

Answer:

(c) bijective

Question 50.

If f(x) = (ax^{2} – b)^{3}, then the function g such that f{g(x)} = g{f(x)} is given by

(a) g(x)=(b−x1/3a)1/2

(b) g(x)=1(ax2+b)3

(c) g(x)=(ax2+b)1/3

(d) g(x)=(x1/3+ba)1/2

Answer:

(d) g(x)=(x1/3+ba)1/2