JEE MAIN Sets and Relations Previous Year Question Paper and Solution with PDF

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Previous Year Questions
JEE MAIN

JEE MAIN Previous Year Questions (PYQs)

JEE MAIN Sets And Relations PYQ

Qus : 1 JEE MAIN PYQ

Consider function f : A $\to$ B and g : B $\to$ C (A, B, C $ \subseteq $ R) such that (gof)^$-$1 exists, then :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (25 July Evening Shift) PYQ

Solution

Qus : 2 JEE MAIN PYQ

Let $A={-3,-2,-1,0,1,2,3}$ and $R$ be a relation on $A$ defined by $xRy$ iff $2x-y\in{0,1}$. Let $l$ be the number of elements in $R$. Let $m$ and $n$ be the minimum number of elements required to be added in $R$ to make it reflexive and symmetric relations, respectively. Then $l+m+n$ is equal to

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (4 April Evening Shift) PYQ

Solution

Qus : 3 JEE MAIN PYQ

Let $A, B$ and $C$ be sets such that $\varnothing \ne A\cap B \subseteq C$. Which of the following statements is not true?

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (12 April Evening Shift) PYQ

Solution

Qus : 4 JEE MAIN PYQ

Let $R=\{(1,2),(2,3),(3,3)\}$ be a relation on the set $\{1,2,3,4\}$. The minimum number of ordered pairs that must be added to $R$ so that it becomes an equivalence relation is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (23 January Morning Shift) PYQ

Solution

Qus : 5 JEE MAIN PYQ

If {p} denotes the fractional part of the number p, then $\left\{ {{{{3^{200}}} \over 8}} \right\}$, is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 6 September 2020 (Morning) PYQ

Solution

Qus : 6 JEE MAIN PYQ

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 $A\,R_{1}\,B \iff (A\cap B^{c})\cup(B\cap A^{c})=\varnothing$ and $A\,R_{2}\,B \iff A\cup B^{c}=B\cup A^{c}$, for all $A,B\in P(S)$. Then:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (1 February Evening Shift) PYQ

Solution

Qus : 7 JEE MAIN PYQ

Let X = ℝ × ℝ. Define a relation R on X by (a₁,b₁) R (a₂,b₂) ⇔ b₁ = b₂. Statement I: R is an equivalence relation. Statement II: For some (a,b) ∈ X, the set S = { (x,y) ∈ X : (x,y) R (a,b) } represents a line parallel to y = x.

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (23 January Evening Shift) PYQ

Solution

Qus : 8 JEE MAIN PYQ

$ \text{Let } R_1 \text{ and } R_2 \text{ be two relations defined on } \mathbb{R} \text{ by } a R_1 b \Leftrightarrow ab \ge 0 \text{ and } aR_2b \Leftrightarrow a \ge b. \text{ Then,}$

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (27 July Morning Shift) PYQ

Solution

Qus : 9 JEE MAIN PYQ

Let $\mathrm{A}=\{(x, y) \in \mathbf{R} \times \mathbf{R}:|x+y| \geqslant 3\}$ and $\mathrm{B}=\{(x, y) \in \mathbf{R} \times \mathbf{R}:|x|+|y| \leq 3\}$. If $\mathrm{C}=\{(x, y) \in \mathrm{A} \cap \mathrm{B}: x=0$ or $y=0\}$, then $\sum_{(x, y) \in \mathrm{C}}|x+y|$ is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (23 January Evening Shift) PYQ

Solution

Qus : 10 JEE MAIN PYQ

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 $R_2 = {(a, b), (b, a), (c, c), (c, a), (a, a), (b, b), (a, c)}$. Then :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Morning Shift) PYQ

Solution

Qus : 11 JEE MAIN PYQ

Let $S=\{1,2,3,\ldots,10\}$. Suppose $M$ is the set of all the subsets of $S$, then the relation $R=\{(A,B): A\cap B\ne \phi;\ A,B\in M\}$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (27 January Morning Shift) PYQ

Solution

Qus : 12 JEE MAIN PYQ

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

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (28 July Morning Shift) PYQ

Solution

Qus : 13 JEE MAIN PYQ

Let $A={,x\in(0,\pi)-{\tfrac{\pi}{2}}: \log_{(2/\pi)}|\sin x|+\log_{(2/\pi)}|\cos x|=2,}$ and $B={,x\ge 0:\sqrt{x}(\sqrt{x}-4)-3|\sqrt{x}-2|+6=0,}$. Then $n(A\cup B)$ is equal to

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (24 January Evening Shift) PYQ

Solution

Qus : 14 JEE MAIN PYQ

Let $A$ and $B$ be two finite sets with $m$ and $n$ elements respectively. The total number of subsets of the set $A$ is $56$ more than the total number of subsets of $B$. Then the distance of the point $P(m,n)$ from the point $Q(-2,-3)$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (27 January Evening Shift) PYQ

Solution

Qus : 15 JEE MAIN PYQ

Let the number of elements in sets

and

be five and two respectively. Then the number of subsets of

X B each having at least 3 and at most 6 elements is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (8 April Morning Shift) PYQ

Solution

Qus : 16 JEE MAIN PYQ

The set $A={1,2,3,4,5,6,7}$. The relation $R={(x,y)\in A\times A:\ x+y=7}$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (8 April Evening Shift) PYQ

Solution

Qus : 17 JEE MAIN PYQ

Let $S=\{1,2,3,\ldots,100\}$. The number of non-empty subsets $A$ of $S$ such that the product of elements in $A$ is even is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (12 January Morning Shift) PYQ

Solution

Qus : 18 JEE MAIN PYQ

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

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (29 July Morning Shift) PYQ

Solution

Qus : 19 JEE MAIN PYQ

Let $A={,n\in[100,700]\cap\mathbb N:\ n\text{ is neither a multiple of }3\text{ nor a multiple of }4,}$. Then the number of elements in $A$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (6 April Morning Shift) PYQ

Solution

Qus : 20 JEE MAIN PYQ

The relation $R={(x,y): x,y\in\mathbb{Z}\ \text{and}\ x+y\ \text{is even}}$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (28 January Morning Shift) PYQ

Solution

Qus : 21 JEE MAIN PYQ

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 :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (26 February Morning Shift) PYQ

Solution

Qus : 22 JEE MAIN PYQ

Let the relations $R_1$ and $R_2$ on the set $X={1,2,3,\ldots,20}$ be given by $R_1={(x,y):,2x-3y=2}$ and $R_2={(x,y):,-5x+4y=0}$. If $M$ and $N$ are the minimum numbers of ordered pairs that must be added to $R_1$ and $R_2$, respectively, to make them symmetric, then $M+N$ equals:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (6 April Morning Shift) PYQ

Solution

Qus : 23 JEE MAIN PYQ

Let $A = \{ x \in R:|x + 1| < 2\} $ and $B = \{ x \in R:|x - 1| \ge 2\} $. Then which one of the following statements is NOT true?

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (25 June Evening Shift) PYQ

Solution

Qus : 24 JEE MAIN PYQ

Let $R$ be a relation on $\mathbb{Z}\times\mathbb{Z}$ defined by $(a,b)R(c,d)$ iff $ad-bc$ is divisible by $5$. Then $R$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (29 January Morning Shift) PYQ

Solution

Qus : 25 JEE MAIN PYQ

Let Z be the set of all integers,$A = \{ (x,y) \in Z \times Z:{(x - 2)^2} + {y^2} \le 4\} $, $B = \{ (x,y) \in Z \times Z:{x^2} + {y^2} \le 4\} $, $C = \{ (x,y) \in Z \times Z:{(x - 2)^2} + {(y - 2)^2} \le 4\} $, If the total number of relation from A $\cap$ B to A $\cap$ C is 2^p, then the value of p is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (27 August Evening Shift) PYQ

Solution

Qus : 26 JEE MAIN PYQ

Let $A = \{ 1,2,3,....,10\} $ and $$f:A \to A$$ be defined as $f(k) = \left\{ {\matrix{ {k + 1} & {if\,k\,is\,odd} \cr k & {if\,k\,is\,even} \cr } } \right. $ Then the number of possible functions $g:A \to A$ such that $gof = f$ is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (26 February Evening Shift) PYQ

Solution

Qus : 27 JEE MAIN PYQ

Let $A={1,2,3,4,5}$. Let $R$ be a relation on $A$ defined by $xRy$ iff $4x \le 5y$. Let $m$ be the number of elements in $R$, and $n$ be the minimum number of elements from $A \times A$ that are required to be added to $R$ to make it symmetric. Then $m+n$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (6 April Evening Shift) PYQ

Solution

Qus : 28 JEE MAIN PYQ

Let $\mathbb{N}$ denote the set of all natural numbers. Define two binary relations on $\mathbb{N}$ as $R_1 = {(x,y) \in \mathbb{N} \times \mathbb{N} : 2x + y = 10}$ and $R_2 = {(x,y) \in \mathbb{N} \times \mathbb{N} : x + 2y = 10}$. Then:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (16 April Morning Shift) PYQ

Solution

Qus : 29 JEE MAIN PYQ

If $R$ is the smallest equivalence relation on the set $\{1,2,3,4\}$ such that $\{(1,2),(1,3)\}\subset R$, then the number of elements in $R$ is ____.

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (29 January Evening Shift) PYQ

Solution

Qus : 30 JEE MAIN PYQ

The number of elements in the set {x $\in$ R : (|x| $-$ 3) |x + 4| = 6} is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (16 March Morning Shift) PYQ

Solution

Qus : 31 JEE MAIN PYQ

Let $A = \{2, 3, 4\}$ and $B = \{8, 9, 12\}$. Then the number of elements in the relation $R = \{ ((a_1, b_1), (a_2, b_2)) \in (A \times B, A \times B) : a_1 \text{ divides } b_2 \text{ and } a_2 \text{ divides } b_1 \}$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (10 April Evening Shift) PYQ

Solution

Qus : 32 JEE MAIN PYQ

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

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (12 January Evening Shift) PYQ

Solution

Qus : 33 JEE MAIN PYQ

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

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (24 January Morning Shift) PYQ

Solution

Qus : 34 JEE MAIN PYQ

If $R = \{(x,y) : x,y \in \mathbb{Z}, \; x^{2} + 3y^{2} \leq 8 \}$ is a relation on the set of integers $\mathbb{Z}$, then the domain of $R^{-1}$ is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2 September 2020 (Morning) PYQ

Solution

Qus : 35 JEE MAIN PYQ

Let $A={0,1,2,3,4,5}$. Let $R$ be a relation on $A$ defined by $(x,y)\in R$ iff $\max{x,y}\in{3,4}$. Then among the statements $(S_1):$ The number of elements in $R$ is $18$, $(S_2):$ The relation $R$ is symmetric but neither reflexive nor transitive, choose the correct option:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (8 April Evening Shift) PYQ

Solution

Qus : 36 JEE MAIN PYQ

Let A = {2, 3, 4, 5, ....., 30} and '$ \simeq $' be an equivalence relation on A $\times$ A, defined by (a, b) $ \simeq $ (c, d), if and only if ad = bc. Then the number of ordered pairs which satisfy this equivalence relation with ordered pair (4, 3) is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (16 March Evening Shift) PYQ

Solution

Qus : 37 JEE MAIN PYQ

Let $A=\{1,3,4,6,9\}$ and $B=\{2,4,5,8,10\}$. Let $R$ be a relation defined on $A\times B$ such that $R=\{\,((a_1,b_1),(a_2,b_2)) : a_1 \le b_2 \text{ and } b_1 \le a_2 \,\}$. Then the number of elements in the set $R$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (11 April Evening Shift) PYQ

Solution

Qus : 38 JEE MAIN PYQ

Let $R$ be a relation on $\mathbb{Z} \times \mathbb{Z}$ defined by $(a,b) R (c,d)$ if and only if $ad - bc$ is divisible by $5$. Then $R$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (29 January Morning Shift) PYQ

Solution

Qus : 39 JEE MAIN PYQ

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 above statement?

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (17 March Morning Shift) PYQ

Solution

Qus : 40 JEE MAIN PYQ

Let $A={2,3,6,8,9,11}$ and $B={1,4,5,10,15}$. Let $R$ be a relation on $A\times B$ defined by ( ? , ? ) ? ( ? , ? ) ⟺ 3 ? ? − 7 ? ? is an even integer. (a,b)R(c,d)⟺3ad−7bc is an even integer. Then the relation $R$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (8 April Evening Shift) PYQ

Solution

Qus : 41 JEE MAIN PYQ

If $R$ is the smallest equivalence relation on the set ${1,2,3,4}$ such that ${(1,2),(1,3)}\subset R$, then the number of elements in $R$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (29 January Evening Shift) PYQ

Solution

Qus : 42 JEE MAIN PYQ

If the sum of the series $ \dfrac{1}{1(1+d)} + \dfrac{1}{(1+d)(1+2d)} + \dots + \dfrac{1}{(1+9d)(1+10d)} $ is equal to $5$, then $50d$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (9 April Morning Shift) PYQ

Solution

Qus : 43 JEE MAIN PYQ

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 :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (28 June Evening Shift) PYQ

Solution

Qus : 44 JEE MAIN PYQ

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

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (31 August Morning Shift) PYQ

Solution

Qus : 45 JEE MAIN PYQ

Let R₁ and R₂ be two relation defined asfollows :
R₁ = {(a, b) $ \in $ R² : a² + b² $ \in $ Q} and
R₂ = {(a, b) $ \in $ R² : a² + b² $ \notin $ Q},
where Q is theset of all rational numbers. Then :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 3 September 2020 (Evening) PYQ

Solution

Qus : 46 JEE MAIN PYQ

Define a relation R over a class of n $\times$ n real matrices A and B as "ARB iff there exists a non-singular matrix P such that PAP^$-$1 = B". Then which of the following is true?

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (18 March Evening Shift) PYQ

Solution

Qus : 47 JEE MAIN PYQ

Let $R$ be a relation defined on $\mathbb{N}$ as $aRb$ iff $2a+3b$ is a multiple of $5$, $a,b\in\mathbb{N}$. Then $R$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (29 January Evening Shift) PYQ

Solution

Qus : 48 JEE MAIN PYQ

Two newspapers $A$ and $B$ are published in a city. It is known that $25%$ of the city population reads $A$ and $20%$ reads $B$ while $8%$ reads both $A$ and $B$. Further, $30%$ of those who read $A$ but not $B$ look into advertisements and $40%$ of those who read $B$ but not $A$ also look into advertisements, while $50%$ of those who read both $A$ and $B$ look into advertisements. Then the percentage of the population who look into advertisements is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (9 April Evening Shift) PYQ

Solution

Qus : 49 JEE MAIN PYQ

Let a set $A = A_1 \cup A_2 \cup \cdots \cup A_k$, where $A_i \cap A_j = \phi$ for $i \ne j$, $1 \le i, j \le k$. Define the relation $R$ from $A$ to $A$ by $R = {(x,y) : y \in A_i \text{ if and only if } x \in A_i, ; 1 \le i \le k}$. Then, $R$ is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (29 June Morning Shift) PYQ

Solution

Qus : 50 JEE MAIN PYQ

Let $A = {1, 2, 3, \ldots, 100}$ and $R$ be a relation on $A$ such that $R = {(a, b) : a = 2b + 1}$. Let $(a_1, a_2), (a_2, a_3), (a_3, a_4), \ldots, (a_k, a_{k+1})$ be a sequence of $k$ elements of $R$ such that the second entry of an ordered pair is equal to the first entry of the next ordered pair. Then the largest integer $k$, for which such a sequence exists, is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (2 April Evening Shift) PYQ

Solution

Qus : 51 JEE MAIN PYQ

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

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 4 September 2020 (Morning) PYQ

Solution

Qus : 52 JEE MAIN PYQ

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:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (30 January Morning Shift) PYQ

Solution

Qus : 53 JEE MAIN PYQ

Let $\mathrm{A}=\{-3,-2,-1,0,1,2,3\}$. Let R be a relation on A defined by $x \mathrm{R} y$ if and only if $0 \leq x^2+2 y \leq 4$. Let $l$ be the number of elements in R and $m$ be the minimum number of elements required to be added in R to make it a reflexive relation. Then $l+m$ is equal to

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (3 April Morning Shift) PYQ

Solution

Qus : 54 JEE MAIN PYQ

The probability that a relation R from {x, y} to {x, y} is both symmetric and transitive, is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (29 June Evening Shift) PYQ

Solution

Qus : 55 JEE MAIN PYQ

Let $A=\{1,2,3, \ldots, 10\}$ and $B=\left\{\frac{m}{n}: m, n \in A, m< n\right.$ and $\left.\operatorname{gcd}(m, n)=1\right\}$. Then $n(B)$ is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (22 January Morning Shift) PYQ

Solution

Qus : 56 JEE MAIN PYQ

Let $\mathop \cup \limits_{i = 1}^{50} {X_i} = \mathop \cup \limits_{i = 1}^n {Y_i} = T$ 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 exactly 20 of sets X_i’s and exactly 6 of sets Y_i’s, then n is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 4 September 2020 (Evening) PYQ

Solution

Qus : 57 JEE MAIN PYQ

Let $f(x)=x^{2},\ x\in\mathbb{R}$. For any $A\subseteq\mathbb{R}$, define $g(A)={,x\in\mathbb{R}:\ f(x)\in A,}$. If $S=[0,4]$, then which one of the following statements is not true?

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (10 April Morning Shift) PYQ

Solution

Qus : 58 JEE MAIN PYQ

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

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (22 January Morning Shift) PYQ

Solution

Qus : 59 JEE MAIN PYQ

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

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (1 February Evening Shift) PYQ

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Qus : 60 JEE MAIN PYQ

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

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (31 January Morning Shift) PYQ

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Qus : 61 JEE MAIN PYQ

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 be :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 5 September 2020 (Morning) PYQ

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Qus : 62 JEE MAIN PYQ

Let $A={-2,-1,0,1,2,3}$. Let $R$ be a relation on $A$ defined by $xRy$ iff $y=\max{x,1}$. Let $l$ be the number of elements in $R$. Let $m$ and $n$ be the minimum number of elements required to be added in $R$ to make it reflexive and symmetric relations, respectively. Then $l+m+n$ is equal to

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (3 April Evening Shift) PYQ

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Qus : 63 JEE MAIN PYQ

In a class of $140$ students numbered $1$ to $140$, all even–numbered students opted Mathematics, those whose number is divisible by $3$ opted Physics, and those whose number is divisible by $5$ opted Chemistry. The number of students who did not opt for any of the three courses is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (10 January Morning Shift) PYQ

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Qus : 64 JEE MAIN PYQ

Let $A={1,6,11,16,\ldots}$ and $B={9,16,23,30,\ldots}$ be the sets consisting of the first $2025$ terms of two arithmetic progressions. Then $n(A\cup B)$ is

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (4 April Morning Shift) PYQ

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