Sets & Relations — JEE Maths Practice Questions & Solutions

mediumPYQ · JEE Main 2026

Let

A=\{1,4,7\}

and

B=\{2,3,8\}

. The number of elements in the relation

R=\{((a_1,b_1),(a_2,b_2))\in(A\times B)\times(A\times B):a_1+b_2\text{ divides }a_2+b_1\}

is

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easyPYQ · JEE Main 2026

Let

A=\{2,3,4,5,6\}

. Let

R

be a relation on the set

A\times A

given by

(x,y)R(z,w)

if and only if

x

divides

z

and

y\le w

. Then the number of elements in

R

is

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easyPYQ · JEE Main 2026

Let

A=\{(a,b,c):a,b,c\ \text{are non-negative integers and}\ a+b+2c=22\}

. Then

n(A)

is equal to

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hard

Let a relation

R

be defined on the real numbers such that

R = \left\{\left(a,b\right) : \frac ab \in I;\ b \in \left\{\sqrt6,\sqrt{10},\sqrt{15}\right\}\right\},

then

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medium

The relation

R

defined on the set

A = \{1, 2, 3, 4, 5\}

by

R = \{(x, y) : |x^2 - y^2| < 16\}

is given by:

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medium

A survey shows that

63\%

of the Americans like cheese whereas

76\%

like apples. If

x\%

of the Americans like both cheese and apples, then:

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medium

Suppose

A_1, A_2, \ldots, A_{30}

are thirty sets each having

5

elements and

B_1, B_2, \ldots, B_n

are

n

sets each with

3

elements. Let

\bigcup_{i=1}^{30} A_i = \bigcup_{j=1}^{n} B_j = S

, and each element of

S

belongs to exactly

10

of the

A_i

and exactly

9

of the

B_j

. Then

n

is equal to:

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medium

Let

R

be the relation "less than" from

A = \{1, 2, 3, 4\}

to

B = \{1, 3, 5\}

, i.e.

(a, b) \in R \Leftrightarrow a < b

. Then

R \circ R^{-1}

is:

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medium

Let

R

be the real line. Consider the subsets

S = \{(x, y) : y = x + 1,\ 0 < x < 2\}

and

T = \{(x, y) : x - y \text{ is an integer}\}

of the plane

R \times R

. Which one of the following is true?

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medium

Let

S = \{(a, b, c) \in N \times N \times N : a + b + c = 21,\ a \le b \le c\}

and

T = \{(a, b, c) \in N \times N \times N : a, b, c \text{ are in A.P.}\}

, where

N

is the set of all natural numbers. What is the number of elements in

S \cap T

?

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medium

Let

F_1

be the set of parallelograms,

F_2

the set of rectangles,

F_3

the set of rhombuses,

F_4

the set of squares and

F_5

the set of trapeziums in a plane. Then

F_1

may be equal to:

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medium

If

A = \{(x, y) : x^2 + y^2 = 25\}

and

B = \{(x, y) : x^2 + 9y^2 = 144\}

, then

A \cap B

contains:

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medium

For real numbers

x

and

y

, we write

xRy \Leftrightarrow x - y + \sqrt{2}

is an irrational number. Then the relation

R

is:

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medium

Let

R = \{(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)\}

be a relation on the set

A = \{3, 6, 9, 12\}

. The relation is:

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medium

Let

R_1

be the relation defined by

R_1 = \{(a, b) \mid a \ge b,\ a, b \in R\}

. Then

R_1

is:

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medium

Let

A

and

B

be two sets. Then the set

(A-B) \cup (B-A) \cup \left(\overline{A}\cap\overline{B}\right)

is the same as

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medium

Let the finite sets

A

and

B

have

'm'

and

'n'

elements respectively. Given that the total number of subsets of

A

is

56

more than the total number of subsets of

B

, find the value of

(m+n)

.

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easy

The relation

R = \{(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)\}

on the set

A = \{1, 2, 3\}

is:

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easy

The relation

R

is defined in

A = \{1, 2, 3\}

by

aRb

if

|a^2 - b^2| \le 5

. Which of the following is false?

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easy

If

A

is the set of even natural numbers less than

8

and

B

is the set of prime numbers less than

7

, then the number of relations from

A

to

B

is:

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easy

The relation

R

is defined on the set of natural numbers as

\{(a, b) : a = 2b\}

. Then

R^{-1}

is given by:

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easy

If

A = \{1, 2, 3\}

,

B = \{4, 5, 6\}

, which of the following is not a relation from

A

to

B

?

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easy

Let

R

be a relation on the set

N

defined by

\{(x, y) : x, y \in N,\ 2x + y = 41\}

. Then

R

is:

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easy

Let

S

be the set of points inside a square,

T

the set of points inside a triangle and

C

the set of points inside a circle. If the triangle and circle intersect each other and are contained in the square, then:

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easy

If

A = \{1, 3, 5, 7, 9, 11, 13, 15, 17\}

,

B = \{2, 4, \ldots, 18\}

and

N

the set of natural numbers is the universal set, then

A' \cup \big((A \cup B) \cap B'\big)

is:

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easy

The maximum number of equivalence relations on the set

A = \{1, 2, 3\}

is:

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easy

Let

R

be the relation on the set

R

of all real numbers defined by

a\,R\,b

iff

|a - b| \le 1

. Then

R

is:

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easy

Let

R

be a relation in

N

defined by

R = \{(1 + x,\ 1 + x^2) : x \le 5,\ x \in N\}

. Which of the following is false?

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easy

The relation

R = \{(1, 1), (2, 2), (1, 2), (2, 3)\}

on the set

A = \{1, 2, 3\}

is:

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easy

Let

X

and

Y

be two non-empty sets such that

X \cap A = Y \cap A = \phi

and

X \cup A = Y \cup A

for some non-empty set

A

. Then:

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easy

If

R = \{(x, y) \mid x, y \in Z,\ x^2 + y^2 \le 4\}

is a relation in

Z

, then the domain of

R

is:

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easy

Let

A

and

B

be two sets containing four and two elements respectively. Then the number of subsets of the set

A \times B

, each having at least three elements, is:

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easy

If

X

and

Y

are two sets and

X'

denotes the complement of

X

, then

X \cap (X \cup Y)'

is equal to:

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easy

If

A = \{x : x \text{ is a multiple of } 4\}

and

B = \{x : x \text{ is a multiple of } 6\}

, then

A \cap B

consists of all multiples of:

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easy

The relation "less than" in the set of natural numbers is:

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easy

Let

A = \{2, 3, 4, 5\}

and

R = \{(2, 2), (3, 3), (4, 4), (5, 5), (2, 3), (3, 2), (3, 5), (5, 3)\}

be a relation in

A

. Then

R

is:

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easy

Let

R = \{(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)\}

be a relation on the set

A = \{1, 2, 3, 4\}

. The relation

R

is:

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easy

The smallest set

A

such that

A \cup \{1, 2\} = \{1, 2, 3, 5, 9\}

is:

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easy

If

A

and

B

are any two sets, then

A \cup (A \cap B)

is equal to:

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easy

If

A = \{a, b, c\}

,

B = \{b, c, d\}

and

C = \{a, d, c\}

, then

(A - B) \times (B \cap C)

is equal to

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easy

Let

A = \{1, 2, 3, 4\}

, and let

R = \{(2, 2), (3, 3), (4, 4), (1, 2)\}

be a relation on

A

. Then

R

is:

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Sets & Relations — JEE Maths Practice Questions & Solutions

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