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JEE Sets and Relations PYQs with Solutions

242 previous year questions from Sets and Relations (JEE Main & Advanced Mathematics) with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

242 questionsMathematics2004–2026Answers + solutions

About Sets and Relations PYQs

Sets and Relations has 242 previous year questions in the Quantrex Academy JEE Main & Advanced Mathematics bank. The 220 questions in this list come from JEE Main (138), NTA Abhyas JEE Main (35), 99 Percentile Qs Bank for JEE Main (30) and 2 other sources, spanning 2004 to 2026. Each question opens on its own page with the options, the correct answer and the worked solution where available.

Questions by year (this list)

  • 2026: 14
  • 2025: 19
  • 2024: 19
  • 2023: 21
  • 2022: 12
  • 2021: 10
  • 2020: 42
  • 2019: 3
  • 2018: 3
  • 2017: 1
  • 2015: 1
  • 2014: 3

Sets and Relations questions with solutions

1

Let S = \ 1, 2, 3, …, 10\ . Consider the set X = \ R : R is an equivalence relation on the set S such that R has exactly 42 elements \ . Then the number of elements in X is

JEE Advanced 2026 Solution View → 2

Consider the relation R on the set \ -2,-1,0,1,2\ defined by (a, b) ∈ R if and only if 1+ab > 0 . Then, among the statements: I. The number of elements in R is 17 II. R is an

JEE Main 2026 Solution View → 3

Let R = \ (x, y) ∈ ℕ × ℕ : _e(x + y) ≤ 2\ . Then the minimum number of elements, required to be added in R to make it a transitive relation, is __________.

JEE Main 2026 Solution View → 4

Let A = \ 1, 4, 7\ and B = \ 2, 3, 8\ . Then the number of elements, in the relation R = \ ((a_1, b_1), (a_2, b_2)) ∈ ((A × B) × (A × B)) : a_1 + b_2 divides a_2 + b_1\ is _______.

JEE Main 2026 Solution View → 5

Let A = \ 2, 3, 4, 5, 6\ . Let R be a relation on the set A × A given by (x, y) R (z, w) if and only if x divides z and y ≤ w . Then the number of elements in R is _______.

JEE Main 2026 Solution View → 6

Let R be a relation defined on the set \ 1,2,3,4\ ×\ 1,2,3,4\ by R=\ ((a, b),(c, d)): 2 a+3 b=3 c+4 d\ . Then the number of elements in R is

JEE Main 2026 Solution View → 7

Let A=\ 0,1,2, …, 9\ . Let R be a relation on A defined by (x, y) ∈ R if and only if |x-y| is a multiple of 3. Given below are two statements: Statement I : n(R)=36 . Statement II

JEE Main 2026 Solution View → 8

Let A=\ -2,-1,0,1,2,3,4\ . Let R be a relation on A defined by x Ry if and only if 2 x+y 2 . Let l be the number of elements in R. Let m and n be the minimum number of elements

JEE Main 2026 Solution View → 9

The number of elements in the relation R=\ (x, y): 4 x^ 2 +y^ 2 <52, x, y ∈ Z\ is

JEE Main 2026 Solution View → 10

Let S be the set of the first 11 natural numbers. Then the number of elements in A=\ B ⊆ S: n(B) 2 and the product of all elements of B is even \ is \_\_\_\_ .

JEE Main 2026 Solution View → 11

Let the relation R on the set M=\ 1,2,3, …, 16\ be given by R=\ (x, y): 4 y=5 x-3, x, y ∈ M\ . Then the minimum number of elements required to be added in R, in order to make the

JEE Main 2026 Solution View → 12

Let A=\ x:|x^ 2 -10| ≤ 6\ and B=\ x:|x-2|>1\ . Then

JEE Main 2026 Solution View → 13

Let A=\ 2,3,5,7,9\ . Let R be the relation on A defined by x R y if and only if 2 x ≤ 3 y . Let l be the number of elements in R, and m be the minimum number of elements required

JEE Main 2026 Solution View → 14

The number of relations, defined on the set \ a, b, c, d\ , which are both reflexive and symmetric, is equal to:

JEE Main 2026 Solution View → 15

Let the set of all relations R on the set \ a, b, c, d, e, f\ , such that R is reflexive and symmetric, and R contains exactly 10 elements, be denoted by S . Then the number of

JEE Advanced 2025 Solution View → 16

Let A=\ 0,1,2,3,4,5\ . Let R be a relation on A defined by (x, y) ∈ R if and only if max \ x, y\ ∈\ 3,4\ . Then among the statements (S_1) : The number of elements in R is 18

JEE Main 2025 Solution View → 17

The number of relations on the set A=\ 1,2,3\ containing at most 6 elements including (1,2) , which are reflexive and transitive but not symmetric, is ________

JEE Main 2025 Solution View → 18

Let A=\ -3,-2,-1,0,1,2,3\ and R be a relation on A defined by x R y if and only if 2 x-y ∈\ 0,1\ . Let l be the number of elements in R. Let m and n be the minimum number of

JEE Main 2025 Solution View → 19

Let A=\ -2,-1,0,1,2,3\ . let R be a relation on A defined by x R y if and only if y= \ x, 1\ . Let l be the number of elements in R. Let m and n be the minimum number of elements

JEE Main 2025 Solution View → 20

Let A=\ -3,-2,-1,0,1,2,3 , \ . Let R be a relation on A defined by x R y if and only if 0 ≤ x^2+2 y ≤ 4 . Let l be the number of elements in R and m be the minimum number of

JEE Main 2025 Solution View → 21

Let A=\ 1,2,3, …, 10\ and R be a relation on A such that R=\ (a, b): a=2 ~b+1\ . Let (a_1, a_2) , (a_2, a_3),(a_3, a_4) , … ., (a_k, a_ k+1 ) be a sequence of k elements of R such

JEE Main 2025 Solution View → 22

Let A be the set of all functions f: Z arrow Z and R be a relation on A such that R=\ (f, g): f(0)=g(1) and f(1)=g(0)\ . Then R is:

JEE Main 2025 Solution View → 23

Let S=N ∪\ 0\ . Define a relation R from S to R by : R=\ (x, y): _ e y=x _ e ((2)/(5)), x ∈ ~S, y ∈ R\ Then, the sum of all the elements in the range of R is equal to :

JEE Main 2025 Solution View → 24

Define a relation R on the interval \([0, (π)/(2))\) by \(x R y\) if and only if \( ^2 x- ^2 y=1\). Then R is :

JEE Main 2025 Solution View → 25

The relation R=\ (x, y): x, y ∈ ℤ and x+y is even \ is:

JEE Main 2025 Solution View → 26

Let A=\ x ∈(0, π)-\ (π)/(2)\ : _ (2 / π) | x|+ _ (2 / π) | x|=2\ and B=\ x 0: x ( x -4)-3| x -2|+6=0\ . Then n(A ∪ B) is equal to :

JEE Main 2025 Solution View → 27

Let S=\ p_1, p_2 … ., p_ 10 \ be the set of first ten prime numbers. Let A=S ∪ P , where P is the set of all possible products of distinct elements of S . Then the number of all

JEE Main 2025 Solution View → 28

Let A=\ (x, y) ∈ R × R:|x+y| 3\ and B=\ (x, y) ∈ R × R:|x|+|y| ≤ 3\ . If C=\ (x, y) ∈ A ∩ B: x=0 or y=0\ , then ∑_ (x, y) ∈ C |x+y| is :

JEE Main 2025 Solution View → 29

Let X=R × R . Define a relation R on X as : (a_1, b_1) R(a_2, b_2) ⇔ b_1=b_2 Statement I : R is an equivalence relation. Statement II : For some (a, b) ∈ X , the set S=\ (x, y) ∈

JEE Main 2025 Solution View → 30

Let R=\ (1,2),(2,3),(3,3)\ be a relation defined on the set \ 1,2,3,4\ . Then the minimum number of elements, needed to be added in R so that R becomes an equivalence relation, is:

JEE Main 2025 Solution View → 31

Let A=\ 1,2,3\ . The number of relations on A , containing (1,2) and (2,3) , which are reflexive and transitive but not symmetric, is ______ -

JEE Main 2025 Solution View → 32

The number of non-empty equivalence relations on the set \ 1,2,3\ is :

JEE Main 2025 Solution View → 33

Let A=\ 1,2,3, …, 10\ and B=\ (m)/(n): m, n ∈ A, m n. and .gcd(m, n)=1\ . Then n(B) is equal to :

JEE Main 2025 Solution View → 34

If n(X)= ^m C_6 , then the value of m is

JEE Advanced 2024 Solution View → 35

If the value of n(Y)+n(Z) is k^2 , then |k| is Let \(S=\ 1,2,3,4,5,6\ \) and \(X\) be the set of all relations \(R\) from \(S\) to \(S\) that satisfy both the following

JEE Advanced 2024 Solution View → 36

Let A=\ 2,3,6,7\ and B=\ 4,5,6,8\ . Let R be a relation defined on A × B by (a_1, b_1) R (a_2, b_2) if and only ifa_1+a_2=b_1+b_2 . Then the number of elements in R is _________

JEE Main 2024 Solution View → 37

Let A=\ 2,3,6,8,9,11\ and B=\ 1,4,5,10,15\ . Let R be a relation on A × B defined by (a, b) R(c, d) if and only if 3 a d-7 b c is an even integer. Then the relation R is

JEE Main 2024 Solution View → 38

Let A=\ 1,2,3,4,5\ . Let R be a relation on A defined by x R y if and only if 4 x ≤ 5 y . Let m be the number of elements in R and n be the minimum number of elements from A × A

JEE Main 2024 Solution View → 39

Let the relations R_1 and R_2 on the set X=\ 1,2,3, …, 20\ be given by R_1=\ (x, y): 2 x-3 y=2\ and R_2=\ (x, y):-5 x+4 y=0\ . If M and N be the minimum number of elements

JEE Main 2024 Solution View → 40

Let the set S=\ 2,4,8,16, …, 512\ be partitioned into 3 sets A, B, C with equal number of elements such that A ∪ B ∪ C=S and A ∩ B=B ∩ C=A ∩ C=φ . The maximum number of such

JEE Main 2024 Solution View → 41

Let a relation R on N × N be defined as: (x_1, y_1) R(x_2, y_2) if and only ifx_1 ≤ x_2 or y_1 ≤ y_2. Consider the two statements: (I) R is reflexive but not symmetric. (II) R is

JEE Main 2024 Solution View → 42

In a survey of 220 students of a higher secondary school, it was found that at least 125 and at most 130 students studied Mathematics; at least 85 and at most 95 studied Physics

JEE Main 2024 Solution View → 43

Consider the relations R _ 1 and R _ 2 defined as a R _ 1 b ⇔ a ^ 2 + b ^ 2 = 1 for all a, b, ∈ R and (a, b) R _ 2 (c, d) ⇔ a + d = b + c for all (a, b), (c, d) ∈ N × N . Then

JEE Main 2024 Solution View → 44

The number of elements in the set S = \ (x, y, z): x, y, z ∈ Z, x + 2y + 3z = 42, x, y, z ≥ 0\ equals ________

JEE Main 2024 Solution View → 45

Let A = \ 1, 2, 3, . ..20\ . Let R _ 1 and R _ 2 two relation on A such that R _ 1 = (a, b): b is divisible by a R _ 2 = (a, b): a is an integral multiple of b Then, number of

JEE Main 2024 Solution View → 46

Let A = \ 1, 2, 3, . ...100\ . Let R be a relation on A defined by (x, y) ∈ R if and only if 2x = 3y . Let R _ 1 be a symmetric relation on A such that R ⊂ R _ 1 and the number of

JEE Main 2024 Solution View → 47

Let A = \ 1, 2, 3, 4\ and R = \ ( 1, 2 ) , ( 2, 3 ) , ( 1, 4 )\ be a relation on A . Let S be the equivalence relation on A such that R ⊂ S and the number of elements in S is n .

JEE Main 2024 Solution View → 48

The number of symmetric relations defined on the set 1, 2, 3, 4 which are not reflexive is _______.

JEE Main 2024 Solution View → 49

A group of 40 students appeared in an examination of 3 subjects - Mathematics, Physics & Chemistry. It was found that all students passed in at least one of the subjects, 20

JEE Main 2024 Solution View → 50

If R is the smallest equivalence relation on the set 1, 2, 3, 4 such that ( 1, 2 ) , ( 1, 3 ) ⊂ R , then the number of elements in R is ______.

JEE Main 2024 Solution View → 51

Let R be a relation on Z × Z defined by ( a, b ) R ( c, d ) if and only if ad - bc is divisible by 5 . Then R is

JEE Main 2024 Solution View → 52

Let S = 1, 2, 3, … , 10 . Suppose M is the set of all the subsets of S , then the relation R = ( A, B ) : A ∩ B ≠ ϕ; A, B ∈ M is :

JEE Main 2024 Solution View → 53

The number of elements in the set n ∈ ℕ: 10 ≤ n ≤ 100 and 3 ^ n - 3 is a multiple of 7 is _______.

JEE Main 2023 Solution View → 54

Let A = \ 1, 2, 3, 4\ and R be a relation on the set A × A defined by R = \ ((a, b), (c, d)): 2a + 3b = 4c + 5d\ . Then the number of elements in R is _________.

JEE Main 2023 Solution View → 55

Let A = - 4, - 3, - 2, 0, 1, 3, 4 and R = ( a, b ) ∈ A × A : b = | a | or b ^ 2 = a + 1\ be a relation on A . Then the minimum number of elements, that must be added to the

JEE Main 2023 Solution View → 56

The number of relations, on the set \ 1, 2, 3\ containing (1, 2) and (2, 3) which are reflexive and transitive but not symmetric, is _________.

JEE Main 2023 Solution View → 57

Let A = \ 1, 3, 4, 6, 9\ and B = \ 2, 4, 5, 8, 10\ . Let R be a relation defined on A × B such that R = \ ( a _ 1 , b _ 1 ), ( a _ 2 , b _ 2 ): a _ 1 ≤ b _ 2 and b _ 1 ≤ a _ 2 \ .

JEE Main 2023 Solution View → 58

An organization awarded 48 medals in event A ' ' , 25 in event B ' ' and 18 in event C ' ' . If these medals went to total 60 men and only five men got medals in all the three

JEE Main 2023 Solution View → 59

Let A = \ 2, 3, 4\ and B = \ 8, 9, 12\ . Then the number of elements in the relation R = \ (( a _ 1 , b _ 1 ), ( a _ 2 , b _ 2 )) ∈ (A × B, A × B): a _ 1 divides b _ 2 and a _ 2

JEE Main 2023 Solution View → 60

The number of elements in the set \ n ∈ ℤ: | n ^ 2 - 10n + 19| < 6\ is _______ .

JEE Main 2023 Solution View → 61

Let A = 1, 2, 3, 4, 5, 6, 7 . Then the relation R = ( x, y ) ∈ A × A: x + y = 7 is

JEE Main 2023 Solution View → 62

Let the number of elements in sets A and B be five and two respectively. Then the number of subsets of A × B each having at least 3 and at most 6 elements is

JEE Main 2023 Solution View → 63

Let A = \ 0, 3, 4, 6, 7, 8, 9, 10\ and R be the relation defined on A such that R\ (x, y) ∈ A × A: x - yis odd positive integerorx - y = 2\ . The minimum number of elements that

JEE Main 2023 Solution View → 64

In a group of 100 persons 75 speak English and 40 speak Hindi. Each person speaks at least one of the two languages. If the number of persons who speak only English is α and the

JEE Main 2023 Solution View → 65

Let A = \ 1, 2, 3, 4, . . . . . . . . . . 10\ and B = \ 0, 1, 2, 3, 4\ . The number of elements in the relation R = \ ( a, b ) ∈ A × A: 2 (a - b) ^ 2 + 3(a - b) ∈ B\ is __________

JEE Main 2023 Solution View → 66

Let P(S) denote the power set ofS = \ 1, 2, 3, … , 10\ . Define the relations R _ 1 and R _ 2 on P(S) as A R _ 1 B if (A ∩ B ^ c ) ∪ (B ∩ A ^ c )= ϕ and A R _ 2 B if A ∪ B ^ c = B

JEE Main 2023 Solution View → 67

Let R be a relation on ℝ , given by R = (a, b): 3a - 3b + 7 is an irrational number . Then R is

JEE Main 2023 Solution View → 68

Among the relations S = \ (a, b): a, b ∈ R - \ 0\ , 2 + (a)/(b) > 0\ and T = \ (a, b): a, b ∈ R, a ^ 2 - b ^ 2 ∈ Z\ ,

JEE Main 2023 Solution View → 69

Let R be a relation on N × N defined by (a, b)R (c, d) if and only ifad (b - c) = bc (a - d). Then R is

JEE Main 2023 Solution View → 70

The minimum number of elements that must be added to the relation R = ( a, b ) , ( b, c ) on the set a, b, c so that it becomes symmetric and transitive is:

JEE Main 2023 Solution View → 71

Let R be a relation defined on ℕ as a R b is 2a + 3b is a multiple of 5, a, b ∈ ℕ . Then R is

JEE Main 2023 Solution View → 72

The minimum number of elements that must be added to relation R = \ (a, b), (b, c), (b, d)\ on the set \ a, b, c, d\ , so that it is an equivalence relation is

JEE Main 2023 Solution View → 73

The relation R = \ (a, b): gcd(a, b) = 1, 2a ≠ b, a, b ∈ ℤ\ is:

JEE Main 2023 Solution View → 74

In a study about a pandemic, data of 900 persons was collected. It was found that 190 persons had symptom of fever, 220 persons had symptom of cough, 220 persons had symptom of

JEE Advanced 2022 Solution View → 75

Let R be a relation from the set \ 1, 2, 3 … … … , 60\ to itself such that R = (a, b): b = pq , where p, q ≥ 3 are prime numbers . Then, the number of elements in R is

JEE Main 2022 Solution View → 76

For α ∈ N , consider a relation R on N given by R = (x, y): 3x + is a multiple of 7 . The relation R is an equivalence relation if and only if

JEE Main 2022 Solution View → 77

Let R _ 1 and R _ 2 be two relations defined on ℝ by a R _ 1 b ⇔ ab ≥ 0 and a R _ 2 b ⇔ a ≥ b , then

JEE Main 2022 Solution View → 78

Let A = \ 1, 2, 3, 4, 5, 6, 7\ and B =\ 3, 6, 7, 9\ . Then the number of elements in the set \ C ⊆ A: C ∩ B ≠ ϕ\ is ______

JEE Main 2022 Solution View → 79

Let A = \ 1, 2, 3, 4, 5, 6, 7\ . Define B = T ⊆ A : either 1 ∉ T or 2 ∈ T and C = T ⊆ A: T the sum of all the elements of T is a prime number. Then the number of elements in the

JEE Main 2022 Solution View → 80

Let a set A = A _ 1 ∪ A _ 2 ∪ … ∪ A _ k , where A _ i ∩ A _ j = ϕ for i ≠ j; 1 ≤ i, j ≤ k . Define the relation R from A to A by R = (x, y): y ∈ A _ i if and only if x ∈ A _ i , 1

JEE Main 2022 Solution View → 81

Let R _ 1 = \ (a, b) ∈ N × N: |a - b| ≤ 13\ and R _ 2 = \ (a, b) ∈ N × N: |a - b| ≠ 13\ Then on N :

JEE Main 2022 Solution View → 82

Let R _ 1 and R _ 2 be relations on the set \ 1, 2, … , 50\ such that R _ 1 = (p, p ^ n ): p is a prime and n ≥ 0 is an integer and R _ 2 = (p, p ^ n ): p is a prime and n = 0 or

JEE Main 2022 Solution View → 83

Let A = \ 1, a _ 1 , a _ 2 … … a _ 18 , 77\ be a set of integers with 1 < a _ 1 < a _ 2 < … . . < a _ 18 < 77 . Let the set A + A = \ x + y: x, y ∈ A\ contain exactly 39 elements.

JEE Main 2022 Solution View → 84

Let A = \ n ∈ N: H . C . F . (n, 45) = 1\ and let B = \ 2k: k ∈ \ 1, 2, … , 100\ \ . Then the sum of all the elements of A ∩ B is _____.

JEE Main 2022 Solution View → 85

The sum of all the elements of the set \ α ∈ \ 1, 2, … . . 100\ : HCF(α, 24) = 1\ is

JEE Main 2022 Solution View → 86

Which of the following is not correct for relation R on the set of real numbers?

JEE Main 2021 Solution View → 87

Let Z be the set of all integers, A = \ ( x, y ) ∈ Z × Z: ( x - 2 ) ^ 2 + y ^ 2 ≤ 4\ B = \ ( x, y ) ∈ Z × Z: x ^ 2 + y ^ 2 ≤ 4\ and C = \ ( x, y ) ∈ Z × Z: ( x - 2 ) ^ 2 + ( y - 2

JEE Main 2021 Solution View → 88

Out of all the patients in a hospital 89 % are found to be suffering from heart ailment and 98 % are suffering from lungs infection. If K % of them are suffering from both

JEE Main 2021 Solution View → 89

Let N be the set of natural numbers and a relation R on N be defined by R = \ (x, y) ∈ N × N: x ^ 3 - 3 x ^ 2 y - x y ^ 2 + 3 y ^ 3 = 0\ . Then the relation R is

JEE Main 2021 Solution View → 90

Let A = \ n ∈ N ∣ n ^ 2 ≤ n + 10, 000\ , B = \ 3k + 1 ∣ k ∈ N\ and C = \ 2k ∣ k ∈ N\ , then the sum of all the elements of the set A ∩ (B - C) is equal to ________.

JEE Main 2021 Solution View → 91

Define a relation R over a class of n × n real matrices A and B as &quot; ARB iff there exists a non-singular matrix P such that PA P ^ - 1 = B &quot;. Then which of the following

JEE Main 2021 Solution View → 92

In a school, there are three types of games to be played. Some of the students play two types of games, but none play all the three games. Which Venn diagrams can justify the

JEE Main 2021 Solution View → 93

Let A = \ 2, 3, 4, 5, … . , 30\ and ' ≃ ' be an equivalence relation on A × A, defined by (a, b) ≃ (c, d), if and only if ad = bc . Then the number of ordered pairs which satisfy

JEE Main 2021 Solution View → 94

Let R = (P, Q) | P and Q are at the same distance from the origin be a relation, then the equivalence class of (1, - 1) is the set

JEE Main 2021 Solution View → 95

Let A = n ∈ N: n is a 3 - digit number B = \ 9k + 2: k ∈ N\ and C = \ 9k + l: k ∈ N\ for some l(0 < l < 9) . If the sum of all the elements of the set A ∩ (B ∪ C) is 274 × 400

JEE Main 2021 Solution View → 96

Set A has m elements and set B has n elements. If the total number of subsets of A is 112 more than the total number of subsets of B , then the value of m · n is___.

JEE Main 2020 Solution View → 97

A survey shows that 73 % of the persons working in an office like coffee, whereas 65 % like tea. If x denotes the percentage of them, who like both coffee and tea, then x cannot

JEE Main 2020 Solution View → 98

Let ∪ _ i = 1 ^ 50 X _ i = ∪ _ i = 1 ^ n Y _ i = T , where each X _ i contains 10 elements and each Y _ i contains 5 elements. If each element of the set T is an element of

JEE Main 2020 Solution View → 99

A survey shows that 63 % of the people in a city read newspaper A whereas 76 % read news paper B . If x % of the people read both the newspapers, then a possible value of x can be:

JEE Main 2020 Solution View → 100

Let R _ 1 and R _ 2 be two relations defined as follows : R _ 1 = \ (a, b) ∈ R ^ 2 : a ^ 2 + b ^ 2 ∈ Q\ and R _ 2 = \ (a, b) ∈ R ^ 2 : a ^ 2 + b ^ 2 ∉ Q\ , where Q is the set of

JEE Main 2020 Solution View → 101

If R = \ (x, y): x, y ∈ Z, x ^ 2 + 3 y ^ 2 ≤ 8\ is a relation on the set of integers Z , then the domain of R ^ - 1 is

JEE Main 2020 Solution View → 102

Let X = \ n ∈ N: 1 ≤ n ≤ 50\ . If A = \ n ∈ X: nisamultipleof2\ and B = \ n ∈ X: nisamultipleof7\ , then the number of elements in the smallest subset of X , containing both A and

JEE Main 2020 Solution View → 103

If R = \ (x, y) | x, y ∈ ℤ, x^ 2 + y^ 2 ≤ 4\ is a relation in Z , then domain of R is

NTA Abhyas JEE Main 2020 Solution View → 104

In a certain town 25 % families own a cell phone, 15 % families own a scooter and 65 % families own neither a cell phone nor a scooter. If 1500 families own both a cell phone and

NTA Abhyas JEE Main 2020 Solution View → 105

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 are

NTA Abhyas JEE Main 2020 Solution View → 106

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

NTA Abhyas JEE Main 2020 Solution View → 107

The relation R ~is defined in the set \ 1, 2, 3, 4, 5, 6\ as R = \ ( a, b ) : b = a + 1\ , then&

NTA Abhyas JEE Main 2020 Solution View → 108

The shaded region in the given figure represents

NTA Abhyas JEE Main 2020 Solution View → 109

A relation R is defined from 2, 3, 4, 5 to 3, 6, 7, 10 by xRy ⇒ x is relatively prime to y , then domain of R & is

NTA Abhyas JEE Main 2020 Solution View → 110

If A = \ x: x^ 2 - 5x + 6 = 0\ , B = \ 2, 4\ , C = \ 4, 5\ , then A × (B ∩ C) is

NTA Abhyas JEE Main 2020 Solution View → 111

Let P be the relation defined on the set of all real numbers such that P = \ (a, b) : ^ 2 a - ^ 2 b = 1\ . Then P is&

NTA Abhyas JEE Main 2020 Solution View → 112

The number of elements in the set \ (a, b) : a ^ 2 + b ^ 2 = 50; a, b ∈ Z\ , where Z is the set of all integers, is

NTA Abhyas JEE Main 2020 Solution View → 113

Let W denotes the words in the English dictionary. If the relation R is given by R = (x, y) ∈ W × W: thewordxandyhaveatleastoneletterincommon , then R is

NTA Abhyas JEE Main 2020 Solution View → 114

Let S be the set of all real numbers. Then, the relation R = (a, b): 1 + ab > 0 on S is

NTA Abhyas JEE Main 2020 Solution View → 115

If A = \ x ∈ ℝ: |x| < 2\ and B = \ x ∈ ℝ: |x - 2| ≥ 3\ ; then

NTA Abhyas JEE Main 2020 Solution View → 116

If relations R _ 1 and R _ 2 from set A to set B are defined as R _ 1 = \ (1, 2), (3, 4), (5, 6)\ and R _ 2 = \ (2, 1), (4, 3), (6, 5)\ , then n(A ) can be equal to

NTA Abhyas JEE Main 2020 Solution View → 117

If A = \ x: x = 6 ^ n - 5n - 1, n ∈ ℕ\ and B = \ x: x = 25 ( n - 1 ) , n ∈ ℕ\ ,& then

NTA Abhyas JEE Main 2020 Solution View → 118

If A B are two sets such that n(A × B) = 60 n(A) = 12 also n(A ∩ B) = K , then the sum of maximum & minimum possible value of K is

NTA Abhyas JEE Main 2020 Solution View → 119

If the difference between the number of subsets of two sets A and B is 120 , then n (A ) is equal to

NTA Abhyas JEE Main 2020 Solution View → 120

If the difference between the number of subsets of the sets A and B is 120 , then choose the incorrect option.

NTA Abhyas JEE Main 2020 Solution View → 121

Let Z be the set of integers, if A = \ x ∈ ℤ: |x - 3|(x^ 2 - 5x + 6) = 1\ and B = \ x ∈ ℤ: 10 < 3x + 1 < 22\ , then the number of subsets of the set A × B is

NTA Abhyas JEE Main 2020 Solution View → 122

If set A = \ x: tan ⁡ x = sec ⁡ x, x ∈ [0,4π]\ and set B = \ x: ^ 2 ⁡ x = 1, x ∈ [0,4π]\ , then

NTA Abhyas JEE Main 2020 Solution View → 123

The relation& R ~given by& \ (x, y) : x^ 2 - 3xy + 2y^ 2 = 0, ∀ x, y ∈ R\ is

NTA Abhyas JEE Main 2020 Solution View → 124

Let A and B be two sets. The set A has 2016 more subsets than B. If A ∩ B has 3 members, then the number of members in A ∪ B is

NTA Abhyas JEE Main 2020 Solution View → 125

If in a class there are 200 students in which 120 take Mathematics, 90 take Physics, 60 take Chemistry, 50 take Mathematics & Physics, 50 take Mathematics & Chemistry, 43 take

NTA Abhyas JEE Main 2020 Solution View → 126

If A and B are two sets such that n(A) = 2 and n(B) = 4 , then the total number of subsets of A × B not having more than 5 elements are

NTA Abhyas JEE Main 2020 Solution View → 127

A survey shows that 69% students like mathematics, whereas 75% like chemistry. If x% students like both the subjects, then the maximum value of x is

NTA Abhyas JEE Main 2020 Solution View → 128

For two sets A and B , if n(A) = 7, n(B) = 13 and n(A ∩ B) = 5 , then the incorrect statement is

NTA Abhyas JEE Main 2020 Solution View → 129

If A = \ x: x = 3 ^ n - 2n - 1, n ∈ ℕ\ and B = \ x: x = 4(n - 1), n ∈ ℕ\ , then

NTA Abhyas JEE Main 2020 Solution View → 130

If A = \ 1, 3, 5, 7, 9, 11, 13, 15\ , B = \ 2, 4, … , 16\ and N is the universal set, then A ^ ′ ∪ ((A ∪ B) ∩ B ^ ′ ) is (where, N is the set of natural numbers)

NTA Abhyas JEE Main 2020 Solution View → 131

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

NTA Abhyas JEE Main 2020 Solution View → 132

The set (A ∪ B ∪ C) ∩ (A ∩ B^ ′ ∩ C^ ′ ) ^ ′ is equal to

NTA Abhyas JEE Main 2020 Solution View → 133

Consider a relation R defined as aRb if 2 + ab > 0 where a, b are real numbers. Then, the relation R is

NTA Abhyas JEE Main 2020 Solution View → 134

The set (A ∪ B ∪ C) ∩ (A ∩ B ^ ′ ∩ C ^ ′ ) ^ ′ ∩ C is equal to

NTA Abhyas JEE Main 2020 Solution View → 135

For any two sets A and B, the values of [(A - B) ∪ B] ^ C is equal to

NTA Abhyas JEE Main 2020 Solution View → 136

For two sets A and B , if n (A) = 20, n (B) = 18 and n (A ∩ B) = 5 , then n(A - B) is equal to

NTA Abhyas JEE Main 2020 Solution View → 137

Let n ( A ) denotes the number of elements in the set A . If n(A) = 4, n(B) = 5 and n(A ∩ B) = 3 , then n [ ( A × B ) ∩ ( B × A ) ] is equal to

NTA Abhyas JEE Main 2020 Solution View → 138

Let A, B and C be sets such that ϕ ≠ A ∩ B ⊆ C . Then which of the following statements is not true?

JEE Main 2019 Solution View → 139

Let Z be the set of integers. If A = \ x ∈ Z: 2 ^ (x + 2)( x ^ 2 - 5x + 6) = 1\ and B = x ∈ Z: - 3 < 2x - 1 < 9 , then the number of subsets of the set A × B , is :

JEE Main 2019 Solution View → 140

In a class of 140 students numbered 1 to 140 , all even numbered students opted Mathematics course, those whose number is divisible by 3 opted Physics course and those whose

JEE Main 2019 Solution View → 141

Let N denote the set of all natural numbers. Define two binary relations on N as R _ 1 = \ (x, y) ∈ N × N: 2x + y = 10\ and R _ 2 = \ (x, y) ∈ N × N: x + 2y = 10\ . Then

JEE Main 2018 Solution View → 142

Consider the following two binary relations on the set A=\ a, b, c\ : R_1=\ (c, a)(b, b),(a, c),(c , c),(b, c),(a, a)\ and R_2=\ (a, b),(b, a),(c, c) , (c, a), (a, a), (b, b), (a

JEE Main 2018 Solution View → 143

Consider the following two binary relations on the set A = \ a, b, c\ : R _ 1 = \ (c, a), (b, b), (a, c), (c, c), (b, c), (a, a)\ and R _ 2 = \ (a, b), (b, a), (c, c), (c, a), (a

JEE Main 2018 Solution View → 144

Let S = \ 1,2, 3, … . 9\ . For k = 1,2, … 5, let N _ k be the number of subsets of S , each containing five elements out of which exactly k are odd. Then N _ 1 + N _ 2 + N _ 3 + N

JEE Advanced 2017 Solution View → 145

In a certain town, 25 % of the families own a phone and 15 % own a car; 65 % families own neither a phone nor a car and 2000 families own both a car and a phone. Consider the

JEE Main 2015 Solution View → 146

A relation on the set A=\ x:|x| < 3, x ∈ Z\ , where Z is the set of integers is defined by R=\ (x, y): y=|x|, x ≠-1\ . Then the number of elements in the power set of R is:

JEE Main 2014 Solution View → 147

Let P be the relation defined on the set of all real numbers such that P = \ (a, b): sec ^ 2 a - ^ 2 b = 1\ . Then, P is

JEE Main 2014 Solution View → 148

If X = \ 4 ^ n - 3n - 1: n ∈ N\ and Y = \ 9(n - 1): n ∈ N\ , where N is the set of natural numbers, then X ∪ Y is equal to

JEE Main 2014 Solution View → 149

Let R=\ (x, y): x, y ∈ N. and .x^2-4 x y+3 y^2=0\ , where N is the set of all natural numbers. Then the relation R is :

JEE Main 2013 Solution View → 150

Let R=\ (3,3)(5,5),(9,9),(12,12),(5,12),(3,9) , (3,12),(3,5)\ be a relation on the set A=\ 3,5,9,12\ . Then, R is :

JEE Main 2013 Solution View → 151

Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of A × B having 3 or more elements is :

JEE Main 2013 Solution View → 152

If A=\ x ∈ z^ + : x < 10. and x is a multiple of 3 or 4\ , where z^ + is the set of positive integers, then the total number of symmetric relations on A is

JEE Main 2012 Solution View → 153

Let X and Y are two events such that P(X ∪ Y=) P X ∩(Y . ) Statement 1: P(X ∩ Y^ = P X^ ∩(Y=0 ). Statement 2: P(X) P Y ∈ 2) P X ∩ Y( )

JEE Main 2012 Solution View → 154

Let R be the set of real numbers This question has Statement -1 and Statement -2 . Of the four choices given after the statements, choose the one that best describes the two

JEE Main 2011 Solution View → 155

Let S=\ 1,2,3,4\ . The total number of unordered pairs of disjoint subsets of S is equal to

JEE Advanced 2010 Solution View → 156

Let S be a non-empty subset of R. Consider the following statement: P : There is a rational number x ∈ S such that x>0 . Which of the following statements is the negation of the

JEE Main 2010 Solution View → 157

Consider the following relations: R=\ (x, y) x, y are real numbers and x= wy for some rational number w \ ; S=\ ((m)/(n), (p)/(q)) m, n, p. and q are integers such that n, q ≠ 0

JEE Main 2010 Solution View → 158

If A, B and C are three sets such that A ∩ B=A ∩ C and A ∪ B=A ∪ C , then

JEE Main 2009 Solution View → 159

Let R be the real line. Consider the following subsets of the plane R × R . S=\ (x, y): y=x+1 and 0 < x < 2\ , T=\ (x, y): x-y is an integer \ . Which one of the following is true?

JEE Main 2008 Solution View → 160

Let W denote the words in the English dictionary. Define the relation R by : R=\ (x, y) ∈ W × W the words x and y have at least one letter in common \ . Then R is

JEE Main 2006 Solution View → 161

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

JEE Main 2005 Solution View → 162

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

JEE Main 2004 Solution View → 163

If a set contains n elements, then its power set will contain

99 Percentile Qs Bank for JEE Main Solution View → 164

Let A, B and C be sets such that ϕ ≠ A ∩ B ⊆ C . Then which of the following statements is not true?

99 Percentile Qs Bank for JEE Main Solution View → 165

A class has 175 students. The following data shows the number of students opting for one or more subjects. Mathematics 100; Physics 70; Chemistry 40; Mathematics and Physics 30

99 Percentile Qs Bank for JEE Main Solution View → 166

Identify the Venn diagram in which shaded area represents the& &#39;Some triangles are not isosceles&#39;, Where T is a set of all triangles and I is the set of all isosceles&

99 Percentile Qs Bank for JEE Main Solution View → 167

Let A = \ x, y, z\ ~and~ B = \ 1, 2\ .~Find the number of relations from~ A into~ B .

99 Percentile Qs Bank for JEE Main Solution View → 168

If X = ( 4 ^ n -3n - 1: n ∈ N) and Y = \ 9( n - 1): n ∈ N\ , then X ∩ Y =

99 Percentile Qs Bank for JEE Main Solution View → 169

If R be a relation from A = 1, 2, 3, 4 to B = 1, 3, 5 such that (a, b) ∈ ℝ ⇔ a < b , then ROR^ - 1 is

99 Percentile Qs Bank for JEE Main Solution View → 170

Let A=[a, b, c, d], B=[1,2,3] . Relation R_1, R_2, R_4 are as follows: aligned & R _ 1 =[( a,1),( b,2),( c,1),( d,2)] and R _ 2 =[( a, 1),( b, 1),( c, 1),( d, 1)] and R _ 3 =[(

99 Percentile Qs Bank for JEE Main Solution View → 171

Suppose A _ 1 , A _ 2 , . . . , A _ 30 are thirty sets each having 5 ~elements and B _ 1 , B _ 2 , . . . . , B _ n are n sets each with 3 elements.~Let &#8746; _ i = 1 ^ 30 A _ i

99 Percentile Qs Bank for JEE Main Solution View → 172

Given A=\ 1,2,3,4,5\ , B=\ 1,4,5\ . If R is a relation from A to B such that (x, y)∈ R with x>y , then range of R is

99 Percentile Qs Bank for JEE Main Solution View → 173

The chances to fail in Physics are 20 \% and the chances to fail in Mathematics are 10 \% . What are the chances to fail in at least one subject?

99 Percentile Qs Bank for JEE Main Solution View → 174

array l If A and B are subsets of universal set X such that n(X)=200, n(A)=90, n(B)=80 , n(A^ ∩ B^ )=40, then n( A ∩ B^ )= array

99 Percentile Qs Bank for JEE Main Solution View → 175

Let \(a, b, c\) be real numbers. A set formed with \(a, b, c\) whose order of occurrence is preassigned is called

99 Percentile Qs Bank for JEE Main Solution View → 176

If a set A has m elements and set B has n elements and the number of injections from A to B is 2520 . Then, m is equal to

99 Percentile Qs Bank for JEE Main Solution View → 177

205 students take an examination of whom 105 pass in English, 70 students pass in Mathematics and 30 students pass in both. How many students fail in both subjects?

99 Percentile Qs Bank for JEE Main Solution View → 178

In a committee of 25 members, each member is proficient either in Mathematics or in Statistics or in both. If 19 of them are proficient in Mathematics and 16 of them are

99 Percentile Qs Bank for JEE Main Solution View → 179

If A and B are any two events of a sample space, then set-theoretic description for the event: "Exactly one of the events A, B to occur" is (Here E^ c denotes the compliment of

99 Percentile Qs Bank for JEE Main Solution View → 180

In a certain town, 25 % families own a phone and 15 % own a car, 65 % families own neither a phone nor a car. 2000 families own both a car and a phone. Consider the following

99 Percentile Qs Bank for JEE Main Solution View → 181

If A=\ (a, b): 4 a=5 b ; a, b ∈\ 1,2,3, … 30\ \ , then the number of such ordered pairs (a, b) is

99 Percentile Qs Bank for JEE Main Solution View → 182

If R = \ (x, y) | x, y ∈ Z, x^ 2 + y^ 2 ≤ 4\ is a relation in Z , then domain of R is

99 Percentile Qs Bank for JEE Main Solution View → 183

The number of elements in the set S=\ x ∈ ℤ : x^2-7 x+6 ≤ 0 and .x^2-3 x>0\ is

99 Percentile Qs Bank for JEE Main Solution View → 184

In a certain town 25 % families own a cell phone, 15 % families own a scooter and 65 % families own neither a cell phone nor a scooter. If 1500 families own both a cell phone and

99 Percentile Qs Bank for JEE Main Solution View → 185

Consider a relation R defined as aRb if 2 + ab > 0 where a, b are real numbers. Then, the relation R is

99 Percentile Qs Bank for JEE Main Solution View → 186

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

99 Percentile Qs Bank for JEE Main Solution View → 187

For two sets A and B , if n(A) = 7, n(B) = 13 and n(A ∩ B) = 5 , then the incorrect statement is

99 Percentile Qs Bank for JEE Main Solution View → 188

If A = \ x: x^ 2 - 5x + 6 = 0\ , B = \ 2, 4\ , C = \ 4, 5\ , then A × ( B ∩ C) is

99 Percentile Qs Bank for JEE Main Solution View → 189

Let P be the relation defined on the set of all real numbers such that P = \ (a, b) : ^ 2 a - ^ 2 b = 1\ . Then P is

99 Percentile Qs Bank for JEE Main Solution View → 190

The number of elements in the set \ (a, b): a ^ 2 + b ^ 2 = 50; a, b ∈ Z\ , where Z is the set of all integers, is

99 Percentile Qs Bank for JEE Main Solution View → 191

Let S be the set of all real numbers. Then, the relation R = (a, b): 1 + ab > 0 on S is

99 Percentile Qs Bank for JEE Main Solution View → 192

If in a class there are 200 students in which 120 take Mathematics, 90 take Physics, 60 take Chemistry, 50 take Mathematics & Physics, 50 take Mathematics & Chemistry, 43 take

99 Percentile Qs Bank for JEE Main Solution View → 193

The set \ -1,0,1\ is not a multiplicative group because of the failure of

Most Important Selected Qs for JEE Advanced Solution View → 194

Let P (S) denote the power set of S = \ 1, 2, 3, … , 10\ . Define the relations R _ 1 ~and R _ 2 ~on P(S) as A R _ 1 B if (A ∩ B^ c ) ∪ (B ∩ A^ c ) = ϕ and A R _ 2 B if A ∪ B^ c =

Most Important Selected Qs for JEE Advanced Solution View → 195

On R , the set of real numbers, a relation ρ is defined as a ρ b if and only if 1+a b>0 . Then,

Most Important Selected Qs for JEE Advanced Solution View → 196

If \(R\) and \(R^1\) are equivalence relations on a set \(A\), then so are the relation

Most Important Selected Qs for JEE Advanced Solution View → 197

A relation ρ on the set of real number R is defined as \ x ρ y: x y>0\ . Then, which of the following is/are true?

Most Important Selected Qs for JEE Advanced Solution View → 198

Let R and S be two equivalence relations on a non-void set A . Then

Most Important Selected Qs for JEE Advanced Solution View → 199

Let A=\ x x^3+x^2-p x+q=0, p, q, ∈ R\ and B=\ x x^2-q x+2=0, q ∈ R\ be the sets. If n(A ∩ B)=2 and x_0 ∈(A-B) , then find the value of |p-q+x_0| . [Note: n(P ∩ Q) denotes number

Most Important Selected Qs for JEE Advanced Solution View → 200

A survey shows that 69% students like mathematics, whereas 75% like chemistry. If x% students like both the subjects, then the maximum value of x is

Most Important Selected Qs for JEE Advanced Solution View →
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Related JEE Mathematics chapters

Application of Derivatives (795)Three Dimensional Geometry (756)Sequences and Series (748)Functions (700)Definite Integration (692)Vector Algebra (616)Differential Equations (586)Continuity and Differentiability (576)Probability (561)Complex Number (551)Binomial Theorem (550)Quadratic Equation (517)

Sets and Relations in other exams

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