Maths MCQ Class 12 Ch-1 | Relations & Functions
MCQ | Class 12 | Ch-1 RELATIONS & FUNCTIONS
CH-1 | CLASS 12 RELATIONS & FUNCTIONS
Q 1) Which of these is not a type of relation?a) Reflexive
b) Surjective
c) Symmetric
d) Transitive
Ans: b
Ans: a
Q 3) Let A = { x1, x2, x3, ……..xm}, B = {
y1, y2, y3,……..yn}, then the total number of non empty relations that can be defined from A to B is
a) mn – 1b) nm – 1
c) mn – 1
d) 2nm – 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)}
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
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)}
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
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
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
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)}
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
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
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
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
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
a) Reflexive relation
b) Symmetric relation
c) Equivalence relation
d) Transitive relation
Ans: a
Q 15) Domain of 
is
a) (-∞ , 2)
b) (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
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
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
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
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)
b) (-8, 8)
c) [1, 8)
d) (1, 8)
Ans: a
a) {2, 4, 8}
b) {2, 4, 6, 8}
c) {2, 4, 6}
d) { 1, 2, 3, 4}
Ans: c
Q 22) The domain of the function y = f(x) = 
is
a) (0, ∞)
b)[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
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
Q 24) The domain of the function y = f(x) =
a) (0, ∞ )
b) (1, ∞)
c) (0,1)
d (- ∞, 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
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.
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, ∞)
b) (1, ∞)
c) (0, 1)
d(- ∞, -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}
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]
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)}
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 the function f(x) = Log|x| is given by
a) x ≠0
b) x >0
c) x<0
d) x ∈ R
Q 32) The domain 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
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
Q 34) The range of f(x) =
a) 1
b) -1
c) {1}
d {-1}
b) -1
c) {1}
d {-1}
Ans: d
Q 35) The range of the function f(x) = |x-1| is
a) (-∞ ,∞)
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
Q 36) The range of the function f(x) =
a) (0,3)
b) [0,3)
c) (0,3)
d) [0,3]
b) [0,3)
c) (0,3)
d) [0,3]
Ans: d
Q 37) The function f : R → R defined by f(x) = 3 – 4x is
a) Onto
b) Not onto
c) Not one - one
d) None of these
Q 37) The function f : 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
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
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
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
(a) f(x) = x3
(b) f(x) = x + 2
(c) f(x) = 2x + 1
(d) f(x) = x2 + 1
Ans: b
Q 59) The number of all one-one functions from the set {1, 2, 3, 4, ……………., n} to itself =
a) n
b) n!
c) n2
d) nn
Q 42) The maximum number of equivalence relations on the set A = {1, 2, 3} are
(a) 1
(b) 2
(c) 3
(d) 5
(a) 1
(b) 2
(c) 3
(d) 5
Ans: d
Q 43) Total number of equivalence relations defined in the set S = {a, b, c} is
(a) 5
(b) 3!
(c) 23
(d) 33
(a) 5
(b) 3!
(c) 23
(d) 33
Ans: a
Q 44) 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
(b) an onto function
(c) a bijection
(d) neither one-one nor onto
Ans: c
Q 45) 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
(b) surjective
(c) bijective
(d) none of these
Ans: c
Q 46) Given set A = {a, b, c). An identity relation in set A is
(a) R = {(a, b), (a, c)}
(b) R = {(a, a), (b, b), (c, c)}
(c) R = {(a, a), (b, b), (c, c), (a, c)}
(d) R= {(c, a), (b, a), (a, a)}
(a) R = {(a, b), (a, c)}
(b) R = {(a, a), (b, b), (c, c)}
(c) R = {(a, a), (b, b), (c, c), (a, c)}
(d) R= {(c, a), (b, a), (a, a)}
Ans: b
Reason: A relation R is an identity relation in set A if for all a ∈ A, there exist (a, a) ∈ R.
Q 47) Set A has 3 elements and the set B has 4 elements. Then the number of injective functions that can be defined from set A to set B is
(a) 144
(b) 12
(c) 24
(d) 64
(a) 144
(b) 12
(c) 24
(d) 64
Ans: c
Reason: Total injective mappings/functions = 4P3 = 4! = 24.
Q 48) Let A = {a, b }. Then number of one-one functions from A to A possible are
(a) 2
(b) 4
(c) 1
(d) 3
(a) 2
(b) 4
(c) 1
(d) 3
Ans: a
Reason: if n(A) = m, then possible one-one functions from A to A are m!
Reason: if n(A) = m, then possible one-one functions from A to A are m!
Q 49) If A = {1, 2, 3} and relation R = {(2, 3)} in A. Then Relation R is
a) Reflexive,
b) Symmetric
c) Transitive.
d) None of these
a) Reflexive,
b) Symmetric
c) Transitive.
d) None of these
Ans: c
Reason: Not reflexive, as (1, 1) ∉ R.
Not symmetric, as (2, 3) ∈ R but (3, 2) ∉ R.
This relation is Transitive, Because: Relation R in a non empty set containing one element is transitive.
Reason: Not reflexive, as (1, 1) ∉ R.
Not symmetric, as (2, 3) ∈ R but (3, 2) ∉ R.
This relation is Transitive, Because: Relation R in a non empty set containing one element is transitive.
Q 50) Let A = {1, 2, 3, 4} and B = {a, b, c}. Then number of one-one functions from A to B are
a) 12
b) 4
c) 0
d) None of these
a) 12
b) 4
c) 0
d) None of these
Ans: c
Reason: Ans 0, Because n(A) > n(B)
Q 51) If n(A) = p, then number of bijective functions from set A to A are
a) p2
b) p!
c) 2p
d) 2p
a) p2
b) p!
c) 2p
d) 2p
Ans: b
Reason: Because If n(A) = p and n(A) = n(B) then the number of bijective functions from A to B is p!
Q 52) Let R be the relation in the set N given by R = {(a, b) : a = b - 2, b > 6}.
a) (2, 4) ∊ R
b) (3, 8) ∊ R
a) (2, 4) ∊ R
b) (3, 8) ∊ R
c) (6, 8) ∊ R
d) (8, 7) ∊ R
Ans: c
Q 53) Let f : R R be defined as f(x) = x5
a) f is one-one onto
b) f is many-one onto
c) f is one-one but not onto
d) f is neither one-one nor onto
a) f is one-one onto
b) f is many-one onto
c) f is one-one but not onto
d) f is neither one-one nor onto
Ans: a
Q 54) The function f : N → N defined by f(x) = x2 + x + 1 is
a) one-one onto
b) one-one but not onto
c) onto but not one-one
d) neither one-one nor onto
b) one-one but not onto
c) onto but not one-one
d) neither one-one nor onto
Ans: b
Q 55) Let f : R → R be defined by f(x) = 
, then f is
a) one-one
b) not one-one
c) identity function
d) zero function
b) not one-one
c) identity function
d) zero function
Ans: b
Solution Hint f(0) = f(26) but 0 ≠ 26 f(x) is not one-one
Solution Hint f(0) = f(26) but 0 ≠ 26 f(x) is not one-one
Q 56) Let f : R → R be defined by f(x) = x4, then
a) f is one-one onto
b) f is many-one onto
c) f is one-one but not onto
d) f is neither one-one nor onto
b) f is many-one onto
c) f is one-one but not onto
d) f is neither one-one nor onto
Ans: d
Q 57) Let f : R → R be defined by f(x) = 3x , then
a) f is one-one onto
b) f is many-one onto
c) f is one-one but not onto
d) f is neither one-one nor onto
b) f is many-one onto
c) f is one-one but not onto
d) f is neither one-one nor onto
Ans: a
Q 58) Let f : R → R be defined by f(x) = 
, then f is
a) one-one
b) onto
c) bijective
c) f is not defined
b) onto
c) bijective
c) f is not defined
Ans: d
Solution Hint
Since at x = 0, f(x) is not defined So f(x) is not defined for all x ∈ R
Solution Hint
Since at x = 0, f(x) is not defined So f(x) is not defined for all x ∈ R
Q 59) The number of all one-one functions from the set {1, 2, 3, 4, ……………., n} to itself =
a) n
b) n!
c) n2
Ans: b
Q 60) Let f : R → R be defined by f(x) = |x|, then
a) f is one-one onto
b) f is many-one onto
c) f is one-one but not onto
d) f is neither one-one nor onto
b) f is many-one onto
c) f is one-one but not onto
d) f is neither one-one nor onto
Ans: d
Q 61) 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
a) 720
b) 120
c) 0
d) none of these
Ans: c
Solution Hint
n(A) < n(B) Every element of set A can have unique image so f is one-one
If f(x) is one-one and n(B) > n(A) then one element in set B do not have their pre-image in set A.
If f(x) is one-one and n(B) > n(A) then one element in set B do not have their pre-image in set A.
Due to this range of f(x) ≠ co-domain
⇒ f(x) is not onto function.
So there is no mapping from A to B for which f(x) is one-one and onto.
So there is no mapping from A to B for which f(x) is one-one and onto.
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