ACADEMIC SESSION, 2025 – 2026
SUBJECT-MATHEMATICS WORKSHEET -1-MCQ
Topic/ Chapter: Relations and Functions.
1 A relation R in a set A is called _______, if (a1, a2) ∈ R implies (a2, a1) ∈
R, for all a1, a2 ∈ A.
(a) symmetric
(b) transitive
(c) equivalence
(d) non-symmetric
2 Let R be a relation on the set N of natural numbers defined by nRm if n
divides m. Then R is
(a) Reflexive and symmetric
(b) Transitive and symmetric
(c) Equivalence
(d) Reflexive, transitive but not symmetric
3 The maximum number of equivalence relations on the set A = {1, 2, 3}
are
(a) 1
(b) 2
(c) 3
(d) 5
4 If 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
5 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
6 If 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
7 Set A has 3 elements, and set B has 4 elements. Then the number of
injective mappings that can be defined from A to B is
(a) 144
(b) 12
(c) 24
(d) 64
8 The function f : R → R defined by f(x) = 3 – 4x is
(a) Onto
(b) Not onto
(c) None one-one
(d) Bijective
9 The relation R in the set of real numbers defined as R = {(a, b) ∈ R × R :
1 + ab > 0} is
(a) reflexive and transitive
(b) symmetric and transitive
(c) reflexive and symmetric
(d) equivalence relation
10 Let the function ‘f ’ be defined by f(x) = 5x2 + 2, ∀ x ∈ R. Then ‘f ’ is
(a) onto function
(b) one-one, onto function
(c) one-one, into function
(d) many-one, into function
11 Let set X = {1, 2, 3} and a relation R is defined in X as : R = {(1, 3), (2,
2), (3, 2)}, then minimum ordered pairs which should be added in
relation R to make it reflexive and symmetric are
(a) {(1, 1), (2, 3), (1, 2)}
(b) {(3, 3), (3, 1), (1, 2)}
(c) {(1, 1), (3, 3), (3, 1), (2, 3)}
(d) None of these
12 Let Z be the set of integers and R be a relation defined in Z such that
aRb if (a – b) is divisible by 5. Then number of equivalence classes are
(a) 2
(b) 3
(c) 4
(d) 5
13 Let R be a relation defined as R = {(x, x), (y, y), (z, z), (x, z)} in set A = {x,
y, z} then relation R is
(a) reflexive
(b) symmetric
(c) transitive
(d) equivalence
14 Let X = {x2 : x ∈ N} and the function f : N → X is defined by f(x) = x2 , x
∈ N. Then this function is
(a) injective only
(b) not bijective
(c) surjective only
(d) bijective
15 A statement of assertion (A) is followed by a statement of reason (R).
Choose the correct answer out of the following choices.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
Assertion (A): In set A = {1, 2, 3} a relation R defined as R = {(1, 1), (2,
2)} is reflexive. Reason (R): A relation R is reflexive in set A if (a, a) R
for all a A.
16 A statement of assertion (A) is followed by a statement of reason (R).
Choose the correct answer out of the following choices.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
Assertion (A): In set A = {a, b, c} relation R in set A, given as R = {(a, c)}
is transitive.
Reason (R): A singleton relation is transitive.
17 Let R be a relation on the set N of natural numbers defined by nRm if n
divides m. Then R is
(a) Reflexive and symmetric
(b) Transitive and symmetric
(c) Equivalence
(d) Reflexive, transitive but not symmetric
18 Let L denote the set of all straight lines in a plane. Let a relation R be
defined by lRm if and only if l is perpendicular to m ∀l, m ∈ L. Then R
is
(a) reflexive
(b) symmetric
(c) transitive
(d) none of these
19 Set A has 3 elements and the set B has 4 elements. Then the number
of injective mappings that can be defined from A to B is
(a) 144
(b) 12
(c) 24
(d) 64
20 Let f : R → R be defined by f (x) = x2 + 1. Then, pre-images of 17 and –
3, respectively, are
(a) φ, {4, – 4}
(b) {3, – 3}, φ
(c) {4, –4}, φ
(d) {4, – 4, {2, – 2}
21 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
22 Consider the non-empty set consisting of children in a family and a
relation R defined as aRb if a is brother of b. Then R is
(a) symmetric but not transitive
(b) transitive but not symmetric
(c) neither symmetric nor transitive
(d) both symmetric and transitive
23 If a relation R on the set {1, 2, 3} be defined by R = {(1, 2)}, then R is
(a) reflexive
(b) transitive
(c) symmetric
(d) none of these
24 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.
25 Let A = {1, 2, 3, ...n} and B = {a, b}. Then the number of surjections
from A into B is
(a) nP2
(b) 2n – 2
(c) 2n – 1
(d) None of these
26 Let f : R → R be defined by f (x) = 1 /x ∀ x ∈ R. Then f is
(a) one-one
(b) onto
(c) bijective
(d) f is not defined
27 Which of the following functions from Z into Z are bijections?
(a) f (x) = x3 .
(b) f (x) = x + 2
(c) f (x) = 2x + 1
(d) f (x) = x 2 + 1
28 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
29 Let X = {-1, 0, 1}, Y = {0, 2} and a function f : X → Y defined by y = 2x4 ,
is
(a) one-one onto
(b) one-one into
(c) many-one onto
(d) many-one into
30 Let A = R – {3}, B = R – {1}. Let f : A → B be defined by f(x)=(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
ANSWERS
1 (a) symmetric
2 (d) Reflexive,
transitive but
not
symmetric
3 (d) 5
4 (c) 0
5 (a) reflexive
but not
symmetric
6 (c) 0
7 (c) 24
8 (c)
9 (d)
10 (d)
11 (c)
12 (d)
13 (a)
14 (d)
15 (d)
16 (a)
17 (d)
18 (b)
19 (c)
20 (c)
21 (c)
22 (c)
23 (b)
24 (b)
25 (b)
26 (d)
27 (b)
28 (d)
29 (c)
30 (a)
