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JEE • MATHEMATICS • RELATIONS

Relations practice · Easy

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Practice format and chapter quiz

These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

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Showing 1-30 of 180 questions
1 Easy
1 of 180
Analyzing +4 | -1
In the set Z\mathrm{Z} of all integers, which of the following relation RR is not an equivalence relation?
View answer and explanation
Correct option: A
x R yx \,R \,y : if x≤yx \leq y
Option A is correct because the relation xRyxRy if x≤yx \leq y is not symmetric. If x≤yx \leq y, it is not necessarily true that y≤xy \leq x.
2 Easy
2 of 180
Analyzing +4 | -1
Let WW denote the words in the English dictionary. Define the relation RR by: R={(x,y)∈W×W∣R=\{(x, y) \in W \times W \mid the words xx and yy have at least one letter in common }\}
View answer and explanation
Correct option: B
Reflexive, symmetric and not transitive
Option B (Reflexive, symmetric and not transitive) is correct because a word always shares a letter with itself (reflexive), if word x shares a letter with word y, then word y shares a letter with word x (symmetric), but it's possible for x to share a letter with y, and y to share a letter with z, without x and z sharing any letters (not transitive).
3 Easy
3 of 180
Analyzing +4 | -1
Let SS be the set of all real numbers. Then, the relation R={(a,  b):1+ab>0}R = \{ \left( {a,\;b} \right):1 + ab > 0\} on SS is
View answer and explanation
Correct option: A
Reflexive and symmetric but not transitive
The correct answer is A (Reflexive and symmetric but not transitive) because the relation satisfies the reflexive and symmetric properties but fails the transitive property.
4 Easy
4 of 180
Understanding +4 | -1
Let XX be a family of sets and RR be a relation on XX defined by ' AA is disjoint from BB '. Then RR is:
View answer and explanation
Correct option: B
Symmetric
Option B (Symmetric) is correct because if set A is disjoint from set B, then set B is also disjoint from set A.
5 Easy
5 of 180
Understanding +4 | -1
If AΔB=A∪BA \Delta B=A \cup B then
View answer and explanation
Correct option: B
A∩B=ϕA \cap B=\phi
Option B (A∩B=ϕA \cap B=\phi) is correct because if AΔB=A∪BA \Delta B = A \cup B, it means that the intersection of A and B is empty.
6 Easy
6 of 180
Application +4 | -1
If A={x:x2−5x+6=0},B={2,4}A=\left\{x: x^2-5 x+6=0\right\}, B=\{2,4\} and C={4,5}C=\{4,5\}, then A×(B∩C)A \times(B \cap C) is
View answer and explanation
Correct option: A
{(2,4),(3,4)}\{(2,4),(3,4)\}
Option A ({ (2,4), (3,4) }) is correct because it represents the Cartesian product of set A and the intersection of sets B and C.
7 Easy
7 of 180
Understanding +4 | -1
For n,m∈N,n/m{n}, {m} \in {N}, {n} / {m} means that n{n} is a factor of m{m}, the relation // is
View answer and explanation
Correct option: D
Reflexive transitive and not symmetric
Option D is correct because the divisibility relation is reflexive (n/n), transitive (if n/m and m/k, then n/k), but not symmetric (n/m does not imply m/n).
8 Easy
8 of 180
Understanding +4 | -1
Let A={x,  y,  z}  and  B={a,  b,  c,  d}A = \left\{ {x,\;y,\;z} \right\}\;and\;B = \left\{ {a,\;b,\;c,\;d} \right\}. Which one of the following is not a relation from A  to  BA\;to\;B?
View answer and explanation
Correct option: D
{(z,  b),  (y,  b),  (a,  d)}\left\{ {\left( {z,\;b} \right),\;\left( {y,\;b} \right),\;\left( {a,\;d} \right)} \right\}
Option D is correct because it contains an element (a, d) where 'a' is not in set A, thus violating the definition of a relation from A to B.
9 Easy
9 of 180
Analyzing +4 | -1
Consider the following two binary relations on the set A={a,b,c}:R1={(c,a)(b,b),(a,c),(c,c),(b,c),(a,a)}A=\{a, b, c\}: R_{1}=\{(\mathrm{c}, a)(b, b),(\mathrm{a}, c),(c, c),(b, c),(a, a)\} and R2={(a,b),(b,a),(c,c),(c,a),(a,a),(b,b),(a,c)R_{2}=\{(a, b),(b, a),(c, c),(c, a),(a, a),(b, b),(a, c). Then
View answer and explanation
Correct option: A
R2R_{2} is symmetric but it is not transitive
Option A (R2R_2 is symmetric but it is not transitive) is correct because R2R_2 satisfies the symmetric property but not the transitive property.
10 Easy
10 of 180
Understanding +4 | -1
In order that a relation RR defined on a non-empty set AA is an equivalence relation. It is sufficient, if RR
View answer and explanation
Correct option: D
possesses all the above three properties
Option D (possesses all the above three properties) is correct because an equivalence relation must be reflexive, symmetric, and transitive.
11 Easy
11 of 180
Analyzing +4 | -1
Let R1R_1 and R2R_2 be two relations defined as follows:

R1={(a,b)∈R2:a2+b2∈Q}R_1=\left\{(a, b) \in R^2: a^2+b^2 \in Q\right\}

and R2={(a,b)∈R2:a2+b2∉Q}.R_2=\left\{(a, b) \in R^2: a^2+b^2 \notin Q\right\}. Then,
View answer and explanation
Correct option: C
neither R1R_1 nor R2R_2 is transitive
The correct answer is C. Neither R1R_1 nor R2R_2 is transitive because counterexamples can be found for both relations.
12 Easy
12 of 180
Application +4 | -1
If f(x)=4x−x2,x∈Rf(x)=4 x-x^2, x \in R, then f(b+1)−f(b−1)f(b+1)-f(b-1) is equal to m(2−b){m}(2-{b}). The value of 'm{m}' is
View answer and explanation
Correct option: A
4
Option A (4) is correct because expanding f(b+1) - f(b-1) and comparing it to m(2-b) gives m = 4.
13 Easy
13 of 180
Understanding +4 | -1
Let L\mathrm{L} denote the set of all straight lines in a plane. Let a relation RR be defined by αRβ⇔α⊥β,α,β∈L\alpha R \beta \Leftrightarrow \alpha \perp \beta, \alpha, \beta \in L. Then, R\mathrm{R} is
View answer and explanation
Correct option: B
Symmetric
Option B (Symmetric) is correct because if line α\alpha is perpendicular to line β\beta, then line β\beta is also perpendicular to line α\alpha.
14 Easy
14 of 180
Analyzing +4 | -1
aRb⇔∣a∣≤ba R b \Leftrightarrow|a| \leq b. Then RR is
View answer and explanation
Correct option: C
Transitive
Option C (Transitive) is correct because if |a| ≤ b and |b| ≤ c, then |a| ≤ c, satisfying the transitive property.
15 Easy
15 of 180
Understanding +4 | -1
Let RR be a relation defined by R={(a,b):a≥b}R=\{(a, b): a \geq b\}, where aa and bb are real numbers, then RR is
View answer and explanation
Correct option: B
reflexive, transitive but not symmetric
Option B (reflexive, transitive but not symmetric) is correct because the relation a≥ba \geq b holds for a=ba=b (reflexive), if a≥ba \geq b and b≥cb \geq c then a≥ca \geq c (transitive), but a≥ba \geq b does not imply b≥ab \geq a (not symmetric).

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16 Easy
16 of 180
Analyzing +4 | -1
Let A={2,3,4}A=\{2,3,4\} and B={8,9,12}B=\{8,9,12\}. Then the number of elements in the relation
R={((a1,b1),(a2,b2))∈(A×B,A×B):a1R=\left\{\left(\left(a_1, b_1\right),\left(a_2, b_2\right)\right) \in(A \times B, A \times B): a_1\right. divides b2b_2 and a2a_2 divides b1}\left.b_1\right\} is
View answer and explanation
Correct option: A
36
Option A (36) is correct because the number of elements in the relation R is calculated by considering all possible pairs (a1, b2) and (a2, b1) where a1 divides b2 and a2 divides b1.
17 Easy
17 of 180
Application +4 | -1
Let RR be the relation in the set N\mathrm{N} given by R={(a,b):a=b−2,b>6}R=\{(a, b): a=b-2, b>6\}. Choose the correct answer.
View answer and explanation
Correct option: C
(6,8)∈R(6,8) \in R
Option C ((6,8) ∈ R) is correct because it satisfies the condition a = b - 2 and b > 6.
18 Easy
18 of 180
Analyzing +4 | -1
On the set NN of all natural numbers define the relation RR by aRba R b if and only if the G.C.D. of aa and bb is 2 . then RR is
View answer and explanation
Correct option: B
Symmetric only
Option B (Symmetric only) is correct because if the GCD of a and b is 2, then the GCD of b and a is also 2, but a number's GCD with itself is itself, and transitivity doesn't hold.
19 Easy
19 of 180
Analyzing +4 | -1
If R={(a,b):3a−3b+7R=\{(a, b): 3 a-3 b+\sqrt{7} is irrational}\}. Then which among the following options are correct
View answer and explanation
Correct option: C
RR is reflexive but not symmetric
Option C (RR is reflexive but not symmetric) is correct because the relation satisfies the reflexive property but fails to satisfy the symmetric property.
20 Easy
20 of 180
Understanding +4 | -1
In a set of teachers of a school, two teachers are said to be related if they “teach the same subject”, then the relation is
View answer and explanation
Correct option: D
Equivalence
Option D (Equivalence) is correct because the relation "teach the same subject" is reflexive, symmetric, and transitive, thus it is an equivalence relation.
21 Easy
21 of 180
Application +4 | -1
Given two finite sets AA and BB such that n(A)=2,n(B)=3n(A)=2, n(B)=3. Then total number of relations from AA to BB is?
View answer and explanation
Correct option: C
64
The correct answer is C (64) because the total number of relations from A to B is 2 raised to the power of the cardinality of A cross B.
22 Easy
22 of 180
Understanding +4 | -1
Let RR be an equivalence relation on a finite set A having nn elements. Then, the number of ordered pairs in RR is
View answer and explanation
Correct option: B
Greater than or equal to nn
Option B (Greater than or equal to nn) is correct because an equivalence relation must be reflexive, meaning (a, a) is in R for all a in A, resulting in at least n ordered pairs.
23 Easy
23 of 180
Application +4 | -1
The solution set of 8x≡6( mod 14),x∈Z8 x \equiv 6(\bmod 14), x \in Z, are:
View answer and explanation
Correct option: C
[6]∪[13][6] \cup[13]
The correct answer is C ([6] ∪ [13]) because the solution set consists of equivalence classes that satisfy the given congruence relation.
24 Easy
24 of 180
Understanding +4 | -1
Which of the following relation is NOT a function
View answer and explanation
Correct option: C
h={(n,1n)∣n∈I}h=\left\{\left(n, \frac{1}{n}\right) \mid n \in \mathrm{I}\right\}
Option C (h={(n,1n)∣n∈I}h=\{\left(n, \frac{{1}}{{n}}\right) \mid n \in \mathrm{{I}}\}) is correct because when n=0, 1/n is undefined, thus violating the function definition.
25 Easy
25 of 180
Application +4 | -1
The number of symmetric relations defined on A = {1,2,3,4,5} which are not reflexive
is_____
View answer and explanation
Correct option: A
215−210{2^{15}} - {2^{10}}
Option A (215−210{2^{15}} - {2^{10}}) is correct because it represents the total number of symmetric relations minus the number of reflexive relations on the set A.
26 Easy
26 of 180
Analyzing +4 | -1
Let R  and  SR\;and\;S be two non-void relations on a setA. Which of the following statements is false?
View answer and explanation
Correct option: B
R  and  SR\;and\;S are transitive implies R∪SR \cup S is transitive.
Option B is correct because the union of two transitive relations is not necessarily transitive, as demonstrated by the given counterexample.
27 Easy
27 of 180
Analyzing +4 | -1
Let AA be the non-void set of the children in a family. The relation ' xx is a brother of yy ' on AA is
View answer and explanation
Correct option: C
Transitive
Option C (Transitive) is correct because if x is a brother of y, and y is a brother of z, then x is a brother of z.
28 Easy
28 of 180
Application +4 | -1
Let RR be a relation from the set {1,2,3,….,60}\{1,2,3, \ldots ., 60\} to itself such that R={(a,b):b=pqR=\{(a, b): b=p q, where p,q≥3p, q \geq 3 are prime numbers }\}. Then, the number of elements in RR is:
View answer and explanation
Correct option: B
660
Option B (660) is correct because there are 11 possible values for b (product of two primes >= 3) and 60 possible values for a, resulting in 60*11 = 660 elements.
29 Easy
29 of 180
Understanding +4 | -1
Let A={1,2,3,4}\mathrm{A}=\{1,2,3,4\} and let R={(2,2),(3,3),(4,4)\mathrm{R}=\{(2,2),(3,3),(4,4), (1,2)}(1,2)\} be a relation on AA. Then R\mathrm{R} is
View answer and explanation
Correct option: C
Transitive
Option C (Transitive) is correct because for the given relation R, if (a, b) and (b, c) are in R, then (a, c) is also in R. In this case, the only relevant pair is (1, 2), and there is no (2, x) in R other than (2, 2), and (1, 2) is already in R.
30 Easy
30 of 180
Understanding +4 | -1
The relation R={(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)}\mathrm{R}=\{(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)\} on set A={1,2,3}\mathrm{A}=\{1,2,3\} is
View answer and explanation
Correct option: A
Reflexive but not symmetric
Option C (II and III) is correct because a set lists distinct elements without repetition, and the order of elements does not matter.
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Key Takeaways

  • ✓ This set contains 180 single-correct-answer MCQs on RELATIONS.
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