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## 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
(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
(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
(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) 2106
(c) 106!

Relation And Function Class 12 MCQ Questions Question 5.
If f(x) = (ax2 + b)3, then the function g such that f(g(x)) = g(f(x)) is given by
(a) $$g(x)=\left(\frac{b-x^{1 / 3}}{a}\right)$$
(b) $$g(x)=\frac{1}{\left(a x^{2}+b\right)^{3}}$$
(c) $$g(x)=\left(a x^{2}+b\right)^{1 / 3}$$
(d) $$g(x)=\left(\frac{x^{1 / 3}-b}{a}\right)^{1 / 2}$$
(d) $$g(x)=\left(\frac{x^{1 / 3}-b}{a}\right)^{1 / 2}$$

Relation And Function MCQ Question 6.
If f : R → R, g : R → R and h : R → R is such that f(x) = x2, g(x) = tanx and h(x) = logx, then the value of [ho(gof)](x), if x = $$\frac{\sqrt{\pi}}{2}$$ will be
(a) 0
(b) 1
(c) -1
(d) 10
(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) = x2 + 7, then the value of x for which f(g(x)) = 25 is
(a) ±1
(b) ±2
(c) ±3
(d) ±4
(b) ±2

Class 12 Maths Chapter 1 MCQ Questions Question 8.
Let f : N → R : f(x) = $$\frac{(2 x-1)}{2}$$ and g : Q → R : g(x) = x + 2 be two functions. Then, (gof) ($$\frac{3}{2}$$) is
(a) 3
(b) 1
(c) $$\frac{7}{2}$$
(d) None of these
(a) 3

Relation And Function MCQ Class 12 Question 9.
Let $$f(x)=\frac{x-1}{x+1}$$, then f(f(x)) is
(a) $$\frac{1}{x}$$
(b) $$-\frac{1}{x}$$
(c) $$\frac{1}{x+1}$$
(d) $$\frac{1}{x-1}$$
(b) $$-\frac{1}{x}$$

Class 12 Maths Chapter 1 MCQ Question 10.
If f(x) = $$1-\frac{1}{x}$$, then f(f($$\frac{1}{x}$$))
(a) $$\frac{1}{x}$$
(b) $$\frac{1}{1+x}$$
(c) $$\frac{x}{x-1}$$
(d) $$\frac{1}{x-1}$$
(c) $$\frac{x}{x-1}$$

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) = x2, 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
(a) 0

MCQ Relation And Function Class 12 Question 12.
If f(x) = $$\frac{3 x+2}{5 x-3}$$ then (fof)(x) is
(a) x
(b) -x
(c) f(x)
(d) -f(x)
(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 = $$\frac{a b}{4}$$. Then, $$3 *\left(\frac{1}{5} * \frac{1}{2}\right)$$ is equal to
(a) $$\frac{3}{160}$$
(b) $$\frac{5}{160}$$
(c) $$\frac{3}{10}$$
(d) $$\frac{3}{40}$$
(a) $$\frac{3}{160}$$

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
(c) 16

Relations And Functions MCQ Question 15.
Let * be a binary operation on Q, defined by a * b = $$\frac{3 a b}{5}$$ is
(a) Commutative
(b) Associative
(c) Both (a) and (b)
(d) None of these
(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 = $$\frac{a b}{5}$$. Write the identity for *.
(a) 5
(b) 3
(c) 1
(d) 6
(a) 5

MCQ On Relations And Functions Pdf Question 17.
For binary operation * defind on R – {1} such that a * b = $$\frac{a}{b+1}$$ is
(a) not associative
(b) not commutative
(c) commutative
(d) both (a) and (b)
(d) both (a) and (b)

Class 12 Maths MCQ Chapter 1 Question 18.
The binary operation * defind on set R, given by a * b = $$\frac{a+b}{2}$$ for all a,b ∈ R is
(a) commutative
(b) associative
(c) Both (a) and (b)
(d) None of these
(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
(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
(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
(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
(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
(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
(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
(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
(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
(a) reflexive but not symmetric

Question 28.
The identity element for the binary operation * defined on Q – {0} as a * b = $$\frac{a b}{2}$$ ∀ a, b ∈ Q – {0) is
(a) 1
(b) 0
(c) 2
(d) None of these
(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) $$^{n} P_{2}$$
(b) 2n – 2
(c) 2n – 1
(d) none of these
(b) 2n – 2

Question 30.
Let f : R → R be defind by f(x) = $$\frac{1}{x}$$ ∀ x ∈ R. Then f is
(a) one-one
(b) onto
(c) bijective
(d) f is not defined
(d) f is not defined

Question 31.
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
(b) f(x) = x + 2

Question 32.
Let f : R → R be the functions defined by f(x) = x3 + 5. Then f-1(x) is
(a) $$(x+5)^{\frac{1}{3}}$$
(b) $$(x-5)^{\frac{1}{3}}$$
(c) $$(5-x)^{\frac{1}{3}}$$
(d) 5 – x
(b) $$(x-5)^{\frac{1}{3}}$$

Question 33.
Let f : R – {$$\frac{3}{5}$$} → R be defined by f(x) = $$\frac{3 x+2}{5 x-3}$$. Then
(a) f-1(x) = f(x)
(b) f-1(x) = -f(x)
(c) (fof) x = -x
(d) f-1(x) = $$\frac{1}{19}$$ f(x)
(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) $$\frac{\pi}{4}$$
(b) {nπ + $$\frac{\pi}{4}$$; n ∈ Z}
(c) Does not exist
(d) None of these
(b) {nπ + $$\frac{\pi}{4}$$; 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
(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
(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
(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
(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
(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 = 2x4, is
(a) one-one onto
(b) one-one into
(c) many-one onto
(d) many-one into
(c) many-one onto

Question 41.
Let f : R → R be a function defined by $$f(x)=\frac{e^{|x|}-e^{-x}}{e^{x}+e^{-x}}$$ then f(x) is
(a) one-one onto
(b) one-one but not onto
(c) onto but not one-one
(d) None of these
(d) None of these

Question 42.
Let g(x) = x2 – 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
(b) g is not one-one on R

Question 43.
Let A = R – {3}, B = R – {1}. Let f : A → B be defined by $$f(x)=\frac{x-2}{x-3}$$. 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
(a) f is bijective

Question 44.
The mapping f : N → N is given by f(n) = 1 + n2, 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
(c) one-one but not onto

Question 45.
The function f : R → R given by f(x) = x3 – 1 is
(a) a one-one function
(b) an onto function
(c) a bijection
(d) neither one-one nor onto
(c) a bijection

Question 46.
Let f : [0, ∞) → [0, 2] be defined by $$f(x)=\frac{2 x}{1+x}$$, 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
(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
(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
(a) a bijection

Question 49.
Let f : R → R be a function defined by f(x) = x3 + 4, then f is
(a) injective
(b) surjective
(c) bijective
(d) none of these
(c) bijective

Question 50.
If f(x) = (ax2 – b)3, then the function g such that f{g(x)} = g{f(x)} is given by
(a) $$g(x)=\left(\frac{b-x^{1 / 3}}{a}\right)^{1 / 2}$$
(b) $$g(x)=\frac{1}{\left(a x^{2}+b\right)^{3}}$$
(c) $$g(x)=\left(a x^{2}+b\right)^{1 / 3}$$
(d) $$g(x)=\left(\frac{x^{1 / 3}+b}{a}\right)^{1 / 2}$$
(d) $$g(x)=\left(\frac{x^{1 / 3}+b}{a}\right)^{1 / 2}$$

Question 51.
If f : [1, ∞) → [2, ∞) is given by f(x) = x + $$\frac{1}{x}$$, then f-1 equals to
(a) $$\frac{x+\sqrt{x^{2}-4}}{2}$$
(b) $$\frac{x}{1+x^{2}}$$
(c) $$\frac{x-\sqrt{x^{2}-4}}{2}$$
(d) $$1+\sqrt{x^{2}-4}$$
(a) $$\frac{x+\sqrt{x^{2}-4}}{2}$$

Question 52.
Let f(x) = x2 – x + 1, x ≥ $$\frac{1}{2}$$, then the solution of the equation f(x) = f-1(x) is
(a) x = 1
(b) x = 2
(c) x = $$\frac{1}{2}$$
(d) None of these
(a) x = 1

Question 53.
Which one of the following function is not invertible?
(a) f : R → R, f(x) = 3x + 1
(b) f : R → [0, ∞), f(x) = x2
(c) f : R+ → R+, f(x) = $$\frac{1}{x^{3}}$$
(d) None of these
(d) None of these

Question 54.
The inverse of the function $$y=\frac{10^{x}-10^{-x}}{10^{x}+10^{-x}}$$ is
(a) $$\log _{10}(2-x)$$
(b) $$\frac{1}{2} \log _{10}\left(\frac{1+x}{1-x}\right)$$
(c) $$\frac{1}{2} \log _{10}(2 x-1)$$
(d) $$\frac{1}{4} \log \left(\frac{2 x}{2-x}\right)$$
(b) $$\frac{1}{2} \log _{10}\left(\frac{1+x}{1-x}\right)$$

Question 55.
If f : R → R defind by f(x) = $$\frac{2 x-7}{4}$$ is an invertible function, then find f-1.
(a) $$\frac{4 x+5}{2}$$
(b) $$\frac{4 x+7}{2}$$
(c) $$\frac{3 x+2}{2}$$
(d) $$\frac{9 x+3}{5}$$
(b) $$\frac{4 x+7}{2}$$

Question 56.
Consider the function f in A = R – {$$\frac{2}{3}$$} defiend as $$f(x)=\frac{4 x+3}{6 x-4}$$. Find f-1.
(a) $$\frac{3+4 x}{6 x-4}$$
(b) $$\frac{6 x-4}{3+4 x}$$
(c) $$\frac{3-4 x}{6 x-4}$$
(d) $$\frac{9+2 x}{6 x-4}$$
(a) $$\frac{3+4 x}{6 x-4}$$

Question 57.
If f is an invertible function defined as f(x) = $$\frac{3 x-4}{5}$$, then f-1(x) is
(a) 5x + 3
(b) 5x + 4
(c) $$\frac{5 x+4}{3}$$
(d) $$\frac{3 x+2}{3}$$
(c) $$\frac{5 x+4}{3}$$

Question 58.
If f : R → R defined by f(x) = $$\frac{3 x+5}{2}$$ is an invertible function, then find f-1.
(a) $$\frac{2 x-5}{3}$$
(b) $$\frac{x-5}{3}$$
(c) $$\frac{5 x-2}{3}$$
(d) $$\frac{x-2}{3}$$
(a) $$\frac{2 x-5}{3}$$

Question 59.
Let f : R → R, g : R → R be two functions such that f(x) = 2x – 3, g(x) = x3 + 5. The function (fog)-1 (x) is equal to
(a) $$\left(\frac{x+7}{2}\right)^{1 / 3}$$
(b) $$\left(x-\frac{7}{2}\right)^{1 / 3}$$
(c) $$\left(\frac{x-2}{7}\right)^{1 / 3}$$
(d) $$\left(\frac{x-7}{2}\right)^{1 / 3}$$
(d) $$\left(\frac{x-7}{2}\right)^{1 / 3}$$

Question 60.
Let * be a binary operation on set of integers I, defined by a * b = a + b – 3, then find the value of 3 * 4.
(a) 2
(b) 4
(c) 7
(d) 6
(c) 7

Question 61.
If * is a binary operation on set of integers I defined by a * b = 3a + 4b – 2, then find the value of 4 * 5.
(a) 35
(b) 30
(c) 25
(d) 29
(b) 30

Question 62.
Let * be the binary operation on N given by a * b = HCF (a, b) where, a, b ∈ N. Find the value of 22 * 4.
(a) 1
(b) 2
(c) 3
(d) 4
(b) 2

Question 63.
Consider the binary operation * on Q defind by a * b = a + 12b + ab for a, b ∈ Q. Find 2 * $$\frac{1}{3}$$
(a) $$\frac{20}{3}$$
(b) 4
(c) 18
(d) $$\frac{16}{3}$$
(a) $$\frac{20}{3}$$

Question 64.
The domain of the function $$f(x)=\frac{1}{\sqrt{\{\sin x\}+\{\sin (\pi+x)\}}}$$ where {.} denotes fractional part, is
(a) [0, π]
(b) (2n + 1) π/2, n ∈ Z
(c) (0, π)
(d) None of these
Range of $$f(x)=\sqrt{(1-\cos x) \sqrt{(1-\cos x) \sqrt{(1-\cos x) \ldots \ldots \infty}}}$$