Mathematics
Multiple Choice Questions (MCQ)
MCQ | Class 12 | Chapter 1
RELATIONS AND FUNCTIONS
- 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
Features
- 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.
Action Plan
- 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.
MCQ | CHAPTER 1 | CLASS 12
RELATIONS AND FUNCTIONS
Q 1) Which of these is not a type of relation?
a) Reflexive
b) Surjective
c) Symmetric
d) Transitive
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, ……..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 – 1
b) n
m – 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)}
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
Q 21) Let R be a relation on N defined by x + 2y = 8. The domain of R is
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 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
Q 41) Which of the following functions from Z into Z is bijective?
(a) f(x) =
x3(b) f(x) = x + 2
(c) f(x) = 2x + 1
(d) f(x) =
x2 + 1
Ans: b
Q 42) The maximum number of equivalence relations on the set A = {1, 2, 3} are
(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
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
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
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)}
Ans: b
Reason: A relation R is an identity relation in set A if for all a ∈ A, (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
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
Ans: a
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
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.
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
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
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
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
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
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
Ans: b
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
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
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
Ans: d
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
d) n
n 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
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
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.
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.
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