• MCQ Based on the different types of relations
• MCQ  Based on the different types of functions
• MCQ Based on the Domain and Range of the functions.
• MCQ Based on the general problems based of relations and functions.
• MCQ Based from the CBSE Sample Questions

• In this pdf given below you find the important MCQ which are strictly according to the CBSE syllabus and are very useful for the CBSE Examinations. 
• Solution Hints are also given to some difficult problems. 
• Each MCQ contains four options from which one option is correct. 
• On the right hand side column of the pdf Answer option is given.

• First of all students should Learn and write all basic points and Formulas related to the Relations and Functions.
• Start solving  the NCERT Problems with examples.
• Solve the important assignments on the Relations and Functions.
• Then start solving the following MCQ.

Ans: b

Q 2) A relation is a set of all
a) Ordered pairs
b) Functions
c) y – values
d) None of these 

Ans: a

Q 3) Let A = { x₁, x₂, x₃, ……..x_m}, B = {
y₁, y₂, y₃,……..y_n}, then the total number of non empty relations that can be defined from A to B is

d) 2^nm – 1

 Ans: d

Q 4) Which of the following relations is symmetric but neither reflexive nor transitive for a set A = {1, 2, 3}.
a) R = {(1, 2), (1, 3), (1, 4)}
b) R = {(1, 2), (2, 1)}
c) R = {(1, 1), (2, 2), (3, 3)}
d) R = {(1, 1), (1, 2), (2, 3)} 

Ans: b

Q 5) Let A = {1,2.3} and consider the relation R = { (1, 1), (2, 2), (3, 3), (1, 2)}, then R is
a) Reflexive but not symmetric
b) Reflexive but not transitive
c) Symmetric and transitive
d) Neither symmetric nor transitive 

Ans: a

Q 6) Which of the following relations is transitive but not reflexive for the set S = {3, 4, 6}?
a) R = {(3, 4), (4, 6), (3, 6)}
b) R = {(1, 2), (1, 3), (1, 4)}
c) R = {(3, 3), (4, 4), (6, 6)}
d) R = {(3, 4), (4, 3)} 

Ans: a

Q 7) Let A = {1, 2, 3, 4} and let R be a relation on A given by
R = {(1, 1), (2, 2), (3, 3), (4, 4), (1, 2), (1, 3), (3, 2)} then
a) R is reflexive, symmetric but not transitive.
b) R is reflexive , transitive but not symmetric
c) R is symmetric, transitive but not reflexive
d) R is equivalence relation 

Ans: b

Q 8) Let R be a relation in the set N given by R={(a, b) : a + b = 5, b > 1}. Which of the following will satisfy the given relation?
a) (2, 3) ∈ R
b) (4, 2) ∈ R
c) (2, 1) ∈ R
d) (5, 0) ∈ R 

Ans: a

Q 9) Let A = { 1, 2, 3} and R be a relation defined on A given by R = {(1, 3), (3,1), (3, 3)} then
a) R is symmetric and reflexive
b) R is symmetric and transitive
c) R is symmetric but not reflexive
d) R is reflexive and transitive 

Ans: c

Q 10) Which of the following relations is reflexive and transitive for the set T = {7, 8, 9}?
a) R = {(7, 7), (8, 8), (9, 9)}
b) R = {(7, 8), (8, 7), (8, 9)}
c) R = {0}
d) R = {(7, 8), (8, 8), (8, 9)} 

Ans: a

Q 11) Let A = {1, 2, 3} and R = A X A, then
a) R is not Symmetric
b) R is not reflexive
c) R is not transitive
d) R is an equivalence relation 

Ans: d

Q 12) Let I be a set of all lines in a XY plane and R be a relation in I defined as R = {(I₁, I₂) : I₁ is parallel to I₂}.
What is the type of given relation?
a) Reflexive relation
b) Transitive relation
c) Symmetric relation
d) Equivalence relation 

Ans: d

Q 13) 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
Ans: d
Solution Hint
2x + y = 41
Putting x = y = 1 we get 3 ≠ 41 ⇒ (1, 1) ∉ R ⇒ R is not reflexive
(1, 39) ∈ R but (39, 1) ∉ R ⇒ R is not symmetric 

(18, 5) ∈ R and (5,31) ∈ R but (18,31) ∉ R ⇒ R is not transitive

Q 14)  (a, a) ∈ R, for every a ∈ A. This condition is for which of the following relations?
a) Reflexive relation
b) Symmetric relation
c) Equivalence relation
d) Transitive relation 

Ans: a

Q 15) Domain of   is

a) (-∞ , 2)
b) (2, ∞)

c) (- ∞ , ∞ )

d) None of these 

Ans: a

Q 16) (a₁, a₂) ∈R
implies that (a₂, a₁) ∈ R,
for all a₁, a₂ ∈ A. This condition is for which of the following relations?
a) Equivalence relation
b) Reflexive relation
c) Symmetric relation
d) Universal relation 

Ans: c

Q 17) A function f ∶ N→N is defined by f(x)=x² + 12. What is the type of function here?
a) bijective
b) surjective
c) injective
d) neither surjective nor injective 

Ans: c

Q 18) The following figure depicts which type of function?

a) one-one
b) onto
c) many-one
d) both one-one and onto 

Ans: a

Q 19) The following figure represents which type of function?

a) one-one
b) onto and many one
c) many-one bur not one-one
d) neither one-one nor onto 

Ans: b

Q 20) The domain of    is

a) [1, 8]
b) (-8, 8)
c) [1, 8)
d) (1, 8) 

Ans: a

Ans: c

Q 22) The domain of definition of the function y = f(x) =     is

a) (0, ∞)
b)[0, ∞)

c) (-∞ ,0)

d) (-∞ ,0] 

Ans: d

Q 23) A function f : R→R is defined by f(x)= 5x² – 8. The type of function is
a) one –one
b) onto
c) many-one
d) both one-one and onto 

Ans: c

Q 24) The domain of the function y = f(x) =   is

a) (0, ∞ )

b) (1, ∞)

c) (0,1)
d (- ∞, 1) 

Ans: b

Q 25) The following figure depicts which type of function?

a) injective
b) bijective
c) surjective
d) neither injective nor surjective
Ans: b
Solution Hint 

 The given function is bijective i.e. both one-one and onto.
one – one : Every element in the domain X has a distinct image in the co-domain Y. Thus, the given function is one- one.
onto: Every element in the co- domain Y has a pre- image in the domain X. Thus, the given function is onto.
Q 26) Let A = {1, 2, 3} and B = {4, 5, 6}. Which one of the following functions is bijective?
a) f = {(2, 4), (2, 5), (2, 6)}
b) f = {(1, 5), (2, 4), (3, 4)}
c) f = {(1, 4), (1, 5), (1, 6)}
d) f = {(1, 4), (2, 5), (3, 6)} 

Ans: d

Q 27) The domain of the function f(x)= log(1-x) +   is

a) [-1, 1]
b) (1, ∞)

c) (0, 1)
d(- ∞, -1] 

Ans: d

Q 28) Let P = {10, 20, 30} and Q = {5, 10, 15, 20}. Which one of the following functions is one – one and not onto?
a) f = {(10, 5), (10, 10), (10, 15), (10, 20)}
b) f = {(10, 5), (20, 10), (30, 15)}
c) f = {(20, 5), (20, 10), (30, 10)}
d) f = {(10, 5), (10, 10), (20, 15), (30, 20)} 

Ans: b

Q 29) The domain of the function f(x) =   is

a) R –{2}
b) R
c) R – {0}
d) R – {-2} 

Ans: d

Q 30) Domain of    is

a) [0,4]
b) (0,4)
c) R- (0,4)
d) R- [0,4] 

Ans: a

Q 31) Let M = {5, 6, 7, 8} and N = {3, 4, 9, 10}. Which one of the following functions is neither one-one nor onto?
a) f ={(5, 3), (5, 4), (6, 4), (8, 9)}
b) f = {(5, 3), (6, 4), (7, 9), (8, 10)}
c) f = {(5, 4), (5, 9), (6, 3), (7, 10), (8, 10)}
d) f = {(6, 4), (7, 3), (7, 9), (8, 10)} 

Ans: a

Q 32) The domain of definition of the function f(x) = Log|x| is given by
a) x ≠0
b) x >0
c) x<0
d) x ∈ R 

Ans: a

Q 33) If a relation R on the set {1,2,3} be defined by R = {(1,2)} then R is
a) Transitive
b) None of these
c) Reflexive
d) Symmetric 

Ans: a

Q 34) The range of f(x) =   is

a) 1
b) -1
c) {1}
d {-1} 

Ans: d

Q 35) The range of the function f(x) = |x-1| is
a) (-∞ ,∞)

b) (0, ∞)

c) [0, ∞)

d (- ∞, 0) 

Ans: c

Q 36) The range of the function f(x) =   is

a) (0,3)
b) [0,3)
c) (0,3)
d) [0,3] 

Ans: d

Q 37) The function R : R → R defined by f(x) = 3 – 4x is
a) Onto
b) Not onto
c) Not one – one
d) None of these 

Ans: a

Q 38) The function f : A → B defined by f(x) = 4x + 7, x ∈ R is
(a) one-one
(b) Many-one
(c) Odd
(d) Even 

Ans: a

Q 39) The greatest integer function f(x) = [x] is
(a) One-one
b) Many-one
(c) Both (a) & (b)
d) None of these 

Ans: b

Q 40)   
The number of bijective functions from set A to itself when A contains 72 elements is
(a) 72
(b) (72)²
(c) 72!
(d) 2⁷² 

Ans: c

Ans: b

d) nⁿ