Q JEE MAIN 2026

Let $\mathrm{R}=\left\{(x, y) \in \mathbf{N} \times \mathbf{N}: \log _{\mathrm{e}}(x+y) \leq 2\right\}$. Then the minimum number of elements, required to be...

JEE Main Mathematics Hard

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Q JEE Main 2024

Let a relation R on N x N be defined as : $\left(x_1, y_1\right) R\left(x_2, y_2\right)$ if and only if...

JEE Main Mathematics Easy

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Q JEE MAIN 2024

The number of symmetric relations defined on the set $\{1,2,3,4\}$ which are not reflexive is

JEE Main Mathematics Easy

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Q Jee Main 2024

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...

JEE Main Mathematics Medium

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Q JEE MAIN 2024

Consider the relations $R_1$ and $R_2$ defined as $a R_1 b \Leftrightarrow a^2+b^2=1$ for all $a, b, \in R$ and...

JEE Main Mathematics Easy

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Q JEE MAIN 2026

Let $\mathrm{A}=\{0,1,2, \ldots, 9\}$. Let R be a relation on A defined by $(x, y) \in \mathrm{R}$ if and only...

JEE Main Mathematics Easy

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Q JEE MAIN 2026

Let $R$ be a relation defined on the set $\{1,2,3,4\} \times\{1,2,3,4\}$ by $\mathrm{R}=\{((a, b),(c, d)): 2 a+3 b=3 c+4 d\}$....

JEE Main Mathematics Hard

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Q JEE MAIN_2026_

Let $\mathrm{A}=\{-2,-1,0,1,2,3,4\}$. Let R be a relation on A defined by $x \mathrm{Ry}$ if and only if $...

JEE Main Mathematics Medium

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Q JEE MAIN 2026

The number of elements in the relation $\mathrm{R}=\left\{(x, y): 4 x^2+y^2

JEE Main Mathematics Medium

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Q JEE MAIN_2026

Let the relation $R$ on the set $M=\{1,2,3, \ldots, 16\}$ be given by $$ \mathrm{R}=\{(x, y): 4 y=5 x-3, x,...

JEE Main Mathematics Easy

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Q JEE MAIN 2026

Let $\mathrm{A}=\{2,3,5,7,9\}$. Let R be the relation on A defined by $x \mathrm{R} y$ if and only if $...

JEE Main Mathematics Medium

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Q JEE MAIN 2026

The number of relations, defined on the set $\{\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}\}$, which are both reflexive and symmetric, is equal...

JEE Main Mathematics Easy

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Q JEE Main 2020

If $R=\left\{(x, y) ; x, y \in Z, x^2+3 y^2 \leq 8\right\}$ is a relation on the set of integers...

JEE Main Mathematics Easy

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Q JEE MAIN 2019

Let $A=\{x \in R: x$ is not a positive integer $\}$. Define a function $f: A \rightarrow R$ as $...

JEE Main Mathematics Easy

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Q JEE MAIN 2019

Let $A=\{x \in R: x$ is not a positive integer $\}$. Define a function $f: A \rightarrow R$ as $...

JEE Main Mathematics Easy

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Q JEE MAIN_2021

Let $\mathbb{N}$ be the set of all integers, $$ \begin{aligned} & A=\left\{(x, y) \in \mathbb{Z} \times \mathbb{Z}:(x-2)^2+y^2 \leq 4\right\} \\...

JEE Main Mathematics Easy

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Q JEE-MAIN 2020

Let $R_1$ and $R_2$ be two relation defined as follows : $\mathrm{R}_1=\left\{(\mathrm{a}, \mathrm{b}) \in \mathrm{R}^2: \mathrm{a}^2+\mathrm{b}^2 \in \mathrm{Q}\right\}$ and $...

JEE Main Mathematics Easy

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Q JEE MAIN 2021 S2

Let $N$ be the set of natural numbers and a relation $R$ on $N$ be defined by $...

JEE Main Mathematics Medium

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Q JEE MAIN 2021

Define a relation $R$ over a class of $n \times n$ real matrices $A$ and $B$ as "ARB iff there...

JEE Main Mathematics Hard

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Q JEE MAIN 2021

Let $A \mid=\{2,3,4,5, \ldots ., 30\}$ and ${ }^{\prime} \simeq$ ' be an equivalence relation on $\mathrm{A} \times \mathrm{A}$, defined...

JEE Main Mathematics Easy

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Q JEE MAIN 2022

Let $\mathrm{R}_1=\{(\mathrm{a}, \mathrm{b}) \in \mathrm{N} \times \mathrm{N}:|\mathrm{a}-\mathrm{b}| \leq 13\}$ and $R_2=\{(a, b) \in N \times N:|a-b| \neq 13\}$. Then on...

JEE Main Mathematics Easy

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Q JEE MAIN 2022

Let a set $A=A_1 \cup A_2 \cup \ldots \cup A_{k^{\prime}}$ where $A_i \cap A_j=\phi$ for $...

JEE Main Mathematics Easy

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Q JEE MAIN 2022

Let $R_1$ and $R_2$ be relations on the set $\{1,2, \ldots \ldots, 50\}$ such that $\mathrm{R}_1=\left\{\left(\mathrm{p}, \mathrm{p}^{\mathrm{n}}\right): \mathrm{p}\right.$ is a...

JEE Main Mathematics Medium

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Q JEE-Main 2023

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

JEE Main Mathematics Easy

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Q JEE MAIN 2023

Let A= {–4, –3, –2, 0, 1, 3, 4} and R = {(a, b) ∈ A × A : b...

JEE Main Mathematics Medium

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Q JEE MAIN 2023

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

JEE Main Mathematics Easy

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Q JEE MAIN 2025

Let $\mathrm{A}=\{-3,-2,-1,0,1,2,3\}$ and R be a relation on A defined by $x \mathrm{Ry}$ if and only if $2 x-y \in\{0,1\}$....

JEE Main Mathematics Hard

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Q JEE MAIN 2025

Let . Let R be a relation on defined by if and only if . Let be the number of...

JEE Main Mathematics Medium

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Q JEE MAIN 2025

Let $A=\{1,2,3, \ldots, 100\}$ and $R$ be a relation on $A$ such that $R=\{(a, b): a=2 b+1\}$. Let $...

JEE Main Mathematics Hard

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Q JEE MAIN 2023

Let A = {1, 2, 3, 4} and R be a relation on the set A × A defined by...

JEE Main Mathematics Medium

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Q JEE MAIN 2023

The number of relations, on the set {1, 2, 3} containing (1, 2) and (2,3), which are reflexive and transitive...

JEE Main Mathematics Easy

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Q JEE MAIN 2023

Let A = {0, 3, 4, 6, 7, 8, 9, 10} and R be the relation defined on A such...

JEE Main Mathematics Hard

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Q JEE-Main 2023

Let A={1, 2, 3, 4,.....10} and B = {0, 1, 2, 3, 4}. The number of elements in the relation...

JEE Main Mathematics Medium

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Q JEE MAIN

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 ) $ is and only...

JEE Main Mathematics Hard

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Q JEE-Main 2024

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

JEE Main Mathematics Hard

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Q JEE MAIN 2024

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...

JEE Main Mathematics Easy

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Q JEE MAIN

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 ....

JEE Main Mathematics Medium

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Q JEE MAIN 2024

Let $S=\{1,2,3, \ldots, 10\}$. Suppose M is the set of all the subsets of S , then the relation $...

JEE Main Mathematics Medium

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Q JEE MAIN 2025

The number of relations on the set ${\rm{A}} = \{ 1,2,3\} $, containing at most 6 elements including (1,2), which...

JEE Main Mathematics Hard

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Q JEE MAIN 2025

Let ${\rm{A}} = \{ - 3, - 2, - 1,0,1,2,3\} $. Let R be a relation on A defined by...

JEE Main Mathematics Hard

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Q JEE MAIN 2025

Let A be the set of all functions $f:Z \to Z$ and R be a relation on A such that...

JEE Main Mathematics Medium

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Q JEE MAIN 2025

Let $X=\mathbf{R} \times \mathbf{R}$. Define a relation R on X as : $\left(a_{1}, b_{1}\right) R\left(a_{2}, b_{2}\right) \Leftrightarrow b_{1}=b_{2}$. Statement I:...

JEE Main Mathematics Medium

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Q JEE MAIN 2025

Define a relation R on the interval $\left[ {0,\frac{\pi }{2}} \right)$ by if and only if $...

JEE Main Mathematics Easy

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Q JEE MAIN 2025

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...

JEE Main Mathematics Medium

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Q JEE MAIN 2025

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,...

JEE Main Mathematics Medium

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