CHAPTER 1
RELATIONS AND FUNCTIONS
MULTIPLE CHOICE QUESTIONS
SL.NO. QUESTIONS
1 Let S be the set of all square in a plane with R a relation in S given by
R = {(S1, S2) : S1 is congruent to S2}. Then R is
(a) an equivalence relation.
(b) only reflexive
(c) transitive not symmetric
(d) only symmetric
2 Given set A ={1, 2, 3} and a relation R = {(1, 3), (3, 1)}, the relation R will be
(a) reflexive if (1, 1) is added
(b) symmetric if (2, 3) is added
(c) transitive if (1, 1) is added
(d) symmetric if (3, 2) is added
𝑥
3 The function f :[0,∞) →R given by f(x) = 𝑥+1
(a) f is both one-one and onto
(b) f is one-one but not onto
(c) f is onto but not one-one
(d) neither one-one nor onto
4 Which of the following functions from Z to itself are bijections?
(a) f(x) = x3
(b) f(x)= 𝑥 + 2
(c) f(x) = 2x+1
(d) f(x) = 𝑥 2 + 𝑥
5 Let A ={1,2,3} , B = {1,4,6,9} and R is a relation from A to B define by ‘ x is greater than y ’.
Then range of R is given by:
(a) {1,4,6,9}
(b) {4,6,9}
(c) {1}
(d) none of these
6 Let N be the set of all natural numbers and let R be a relation in N, defined by R = {(a, b)} : a is a
factor of b }.
(a) R is symmetric and transitive but not reflexive
(b) R is reflexive and symmetric but not transitive
(c) R is equivalence
(d) R is reflexive and transitive but not symmetric
7 Let N be the set of all natural numbers and let R be a relation on N × N,defined by (a, b) R (c, d)
⇔ ad = bc.
(a) R is symmetric and transitive but not reflexive
(b) R is reflexive and symmetric but not transitive
(c) R is equivalence
(d) R is reflexive and transitive but not symmetric
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,8 Let A be the set of all points in a plane and let O be the origin. Let
R ={(P, Q) :OP =OQ}. Then, R is
(a) reflexive and symmetric but not transitive
(b) reflexive and transitive but not symmetric
(c) symmetric and transitive but not reflexive
(d) an equivalence relation
9 If f = {(1, 2), ( 3, 5), (4, 1)} and g ={(2, 3), (5, 1), (1, 3)} then (go f ) =?
(a) {(3, 1), (1, 3), (3, 4)}
(b) {(1, 3), (3, 1), (4, 3)}
(c) {(3, 4), (4, 3), (1, 3)}
(d) {(2, 5), (5, 2), (1, 5)}
10 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
11 Set A has 2 elements and the set B has 3 elements. Then the number of relations that can be
defined from set A to set B is
(a) 144
(b) 12
(c) 24
(d) 64
12 Let A be the set of all 50 students of Class X in a school. Let f : A → N be function defined by f (x)
= roll number of the student x.
(a) f is neither one-one nor onto.
(b) f is one-one but not onto
(c ) f is not one-one but onto
(d) none of these
13 Let R be the relation in the set N given by R = {(a, b) : a = b – 3, b > 6}. Choose the correct answer.
(A) (2, 4) 𝜖 R
(B) (3, 8) 𝜀 R
(C) (6, 8) 𝜖R
(D) (4, 7) 𝜖 R
14 The function f : R →R, defined as f (x) = x2, is
(a) neither one-one nor onto
(b) only onto
(c) one-one
(d) none of these
15 Let R be a relation defined on Z as follows: ( x, y)𝜖R ⇔ ǀx−yǀ≤ 1. Then R is:
(a) Reflexive and transitive
(b) Reflexive and symmetric
(c) Symmetric and transitive
(d) an equivalence relation
16. 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
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, (A) Reflexive but not symmetric
(B) Reflexive but not transitive
(C) Symmetric and transitive
Neither symmetric nor transitive
17. Let S be the set of all real numbers. Then the relation R={(a ,b):1+ab>0} on S is
(A) Reflexive and symmetric but not transitive.
(B) Reflexive and transitive but not symmetric.
(C) Symmetric and transitive but not reflexive.
Reflexive, symmetric and transitive.
18 Let R be a relation defined on Z as follows:
(a, b)∈ R⇔a2+b2 =25. Then the domain of R is
(A) {3,4,5}
(B) {0,3,4,5}
(C) {0,±3, ±4, ±5}
None of these
19 If A={a, b, c}, then the relation R={(b, c)} on A is
(A) Reflexive only
(B) Symmetric only
(C) Transitive only
Reflexive and transitive only.
20 Let T be the set of all triangles in the Euclidean plan and let a relation R on T be defined as a R b,
if a is congruent to b, ∀ 𝑎, 𝑏 ∈ 𝑇. Then R is
(A) Reflexive but not transitive
(B) Transitive but not symmetric
(C) Equivalence
None of these
21 Which of the following statement/statements is/are correct?
(A) If R and S are two equivalence relations on a set A, then R ∩ 𝑆 is also an equivalence
relation on A.
(B) The union of two equivalence relations on a set is not necessarily relation on the set.
(C) The inverse of an equivalence relation is an equivalence relation.
All of above
22 Let f: R→ 𝑅 be defined as f(x) =x4.
(A) f is one -one onto
(B) f is many –one onto
(C) f is one-one but not onto
f is neither one-one nor onto
23 Set A has 3 elements and the set B has 4 elements then numbers of injective functions that can
be defined from set A to set B is:
(A) 120
(B) 24
(C) 144
64
24 Consider the set A= {4, 5}. The smallest equivalence relation (i.e. the relation with the least
number of elements), is:
(A) { }
(B) {(4,5)}
(C) {(4,4),(5,5)}
{(4,5),(5,4)}
25. If a function f:[2,∞)→B defined by f(x)=x2 −4x +5 is a bijection , then B=
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