Sets and Relations PYQs - Last 5 Years

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MathematicsAlgebra2022-2026

All Sets and Relations PYQs Last 10 Years Create chapter test

Practice 83 JEE Main Mathematics questions from Sets and Relations. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

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Last 5 Years Sets and Relations Questions

Showing 33 of 83 filtered questions.

1Sets And Relations

Consider the relations $R_1$ and $R_2$ defined as $a R_1 b \Leftrightarrow a^2+b^2=1$ for all $a, b \in \mathbf{R}$ and $(a, b) R_2(c, d) \Leftrightarrow$ $a+d=b+c$ for all $(a, b),(c, d) \in \mathbf{N} \times \mathbf{N}$. Then :

2Sets And Relations

Let \(A=\{0,3,4,6,7,8,9,10\}\) and \(R\) be the relation defined on \(A\) such that \(R=\{(x, y) \in A \times A: x-y\) is odd positive integer or \(x-y=2\}\). The minimum number of elements that must be added to the relation \(R\), so that ...

INTEGER+4 / -12023

3Sets And Relations

Let \(\mathrm{A}=\{1,2,3,4,5,6,7\}\). Then the relation \(\mathrm{R}=\{(x, y) \in \mathrm{A} \times \mathrm{A}: x+y=7\}\) is :

4Sets And Relations

Let \(\mathrm{A}=\{1,2,3,4, \ldots ., 10\}\) and \(\mathrm{B}=\{0,1,2,3,4\}\). The number of elements in the relation \(R=\left\{(a, b) \in A \times A: 2(a-b)^{2}+3(a-b) \in B\right\}\) is ___________.

INTEGER+4 / -12023

5Sets And Relations

Let \(\mathrm{R}\) be a relation on \(\mathrm{N} \times \mathbb{N}\) defined by \((a, b) ~\mathrm{R}~(c, d)\) if and only if \(a d(b-c)=b c(a-d)\). Then \(\mathrm{R}\) is

6Sets And Relations

Among the relations

$\mathrm{S}=\left\{(\mathrm{a}, \mathrm{b}): \mathrm{a}, \mathrm{b} \in \mathbb{R}-\{0\}, 2+\frac{\mathrm{a}}{\mathrm{b}}>0\right\}$
and $\mathrm{T}=\left\{(\mathrm{a}, \mathrm{b}): \mathrm{a}, \mathrm{b} \in \mathbb{R...

7Sets And Relations

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

8Sets And Relations

Let R be a relation defined on \(\mathbb{N}\) as \(a\mathrm{R}b\) if \(2a+3b\) is a multiple of \(5,a,b\in \mathbb{N}\). Then R is

9Sets And Relations

Let S = {1, 2, 3, 5, 7, 10, 11}. The number of non-empty subsets of S that have the sum of all elements a multiple of 3, is _____________.

INTEGER+4 / -12023

10Sets And Relations

The relation \(\mathrm{R = \{ (a,b):\gcd (a,b) = 1,2a \ne b,a,b \in \mathbb{Z}\}}\) is :

11Sets And Relations

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

INTEGER+4 / -12023

12Sets And Relations

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

13Sets And Relations

Let \(P(S)\) denote the power set of \(S=\{1,2,3, \ldots ., 10\}\). Define the relations \(R_{1}\) and \(R_{2}\) on \(P(S)\) as \(\mathrm{AR}_{1} \mathrm{~B}\) if $$\left(\mathrm{A} \cap \mathrm{B}^{\mathrm{c}}\right) \cup\left(\mathrm{B} \...

14Sets And Relations

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

INTEGER+4 / -12023

15Sets And Relations

The number of elements in the set $\left\{n \in \mathbb{N}: 10 \leq n \leq 100\right.$ and $3^{n}-3$ is a multiple of 7$\}$ is ___________.

INTEGER+4 / -12023

16Sets And Relations

Let \(\mathrm{A}=\{-4,-3,-2,0,1,3,4\}\) and \(\mathrm{R}=\left\{(a, b) \in \mathrm{A} \times \mathrm{A}: b=|a|\right.\) or \(\left.b^{2}=a+1\right\}\) be a relation on \(\mathrm{A}\). Then the minimum number of elements, that must be added ...

INTEGER+4 / -12023

17Sets And Relations

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 __________.

INTEGER+4 / -12023

18Sets And Relations

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 events, then, how many received medals in exactly two of three events?

19Sets And Relations

Let \(\mathrm{A}=\{1,3,4,6,9\}\) and \(\mathrm{B}=\{2,4,5,8,10\}\). Let \(\mathrm{R}\) be a relation defined on \(\mathrm{A} \times \mathrm{B}\) such that $$\mathrm{R}=\left\{\left(\left(a_{1}, b_{1}\right),\left(a_{2}, b_{2}\right)\right):...

20Sets And Relations

The number of elements in the set \(\{ n \in Z:|{n^2} - 10n + 19| < 6\}\) is _________.

INTEGER+4 / -12023

21Sets And Relations

Let \(\mathrm{A}=\{2,3,4\}\) and \(\mathrm{B}=\{8,9,12\}\). Then the number of elements in the relation

$$\mathrm{R}=\left\{\left(\left(a_{1}, \mathrm{~b}_{1}\right),\left(a_{2}, \mathrm{~b}_{2}\right)\right) \in(A \times B, A \times B): a...

22Sets And Relations

Let a set A = A1 \(\cup\) A2 \(\cup\) ..... \(\cup\) Ak, where Ai \(\cap\) Aj = \(\phi\) for i \(\ne\) j, 1 \(\le\) j, j \(\le\) k. Define the relation R from A to A by R = {(x, y) : y \(\in\) Ai if and only if x \(\in\) Ai, 1 \(\le\) i $$\...

23Sets And Relations

Let \(S=\{4,6,9\}\) and \(T=\{9,10,11, \ldots, 1000\}\). If \(A=\left\{a_{1}+a_{2}+\ldots+a_{k}: k \in \mathbf{N}, a_{1}, a_{2}, a_{3}, \ldots, a_{k}\right.\) \(\epsilon S\}\), then the sum of all the elements in the set \(T-A\) is equal to...

INTEGER+4 / -12022

24Sets And Relations

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

25Sets And Relations

Let R1 and R2 be relations on the set {1, 2, ......., 50} such that
R1 = {(p, pn) : p is a prime and n \(\ge\) 0 is an integer} and
R2 = {(p, pn) : p is a prime and n = 0 or 1}.
Then, the number of elements in R1 \(-\) R2 is _______________...

INTEGER+4 / -12022

26Sets And Relations

Let R1 = {(a, b) \(\in\) N \(\times\) N : |a \(-\) b| \(\le\) 13} and
R2 = {(a, b) \(\in\) N \(\times\) N : |a \(-\) b| \(\ne\) 13}. Then on N :

27Sets And Relations

For \(\alpha \in \mathbf{N}\), consider a relation \(\mathrm{R}\) on \(\mathbf{N}\) given by \(\mathrm{R}=\{(x, y): 3 x+\alpha y\) is a multiple of 7\(\}\). The relation \(R\) is an equivalence relation if and only if :

28Sets And Relations

Let \(R_{1}\) and \(R_{2}\) be two relations defined on \(\mathbb{R}\) by
\(a \,R_{1} \,b \Leftrightarrow a b \geq 0\) and \(a \,R_{2} \,b \Leftrightarrow a \geq b\)
Then,

29Sets And Relations

Let \(A = \sum\limits_{i = 1}^{10} {\sum\limits_{j = 1}^{10} {\min \,\{ i,j\} } }\) and \(B = \sum\limits_{i = 1}^{10} {\sum\limits_{j = 1}^{10} {\max \,\{ i,j\} } }\). Then A + B is equal to _____________.

INTEGER+4 / -12022

30Sets And Relations

Let A = {n \(\in\) N : H.C.F. (n, 45) = 1} and
Let B = {2k : k \(\in\) {1, 2, ......., 100}}. Then the sum of all the elements of A \(\cap\) B is ____________.

INTEGER+4 / -12022

31Sets And Relations

Let \(A=\{1,2,3,4,5,6,7\}\) and \(B=\{3,6,7,9\}\). Then the number of elements in the set \(\{C \subseteq A: C \cap B \neq \phi\}\) is ___________.

INTEGER+4 / -12022

32Sets And Relations

Let \(A=\{1,2,3,4,5,6,7\}\). Define \(B=\{T \subseteq A\) : either \(1 \notin T\) or \(2 \in T\}\) and \(C=\{T \subseteq A: T\) the sum of all the elements of \(T\) is a prime number \(\}\). Then the number of elements in the set $$B \cup C...

INTEGER+4 / -12022

33Sets And Relations

The sum of all the elements of the set \(\{ \alpha \in \{ 1,2,.....,100\} :HCF(\alpha ,24) = 1\}\) is __________.

INTEGER+4 / -12022