JEE Maths PYQ Practice, chapter-wise

JEE Main 2026 (Online) 8th April Evening ShiftQuestion 31

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

Sets, Relations and Function

Only I is trueOnly II is trueBoth I and II are trueNeither I nor II is true

JEE Main 2024 (Online) 6th April Evening ShiftQuestion 32

Let $A=\{1,2,3,4,5\}$. Let $R$ be a relation on $A$ defined by $xRy$ if and only if $4x\le5y$. 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 a symmetric relation. Then $m+n$ is equal to :

Sets, Relations and Function

$23$$24$$25$$26$

JEE Main 2020 (Online) 8th January Evening ShiftQuestion 33

Let $f:(1,3)\to\mathbf{R}$ be a function defined by $f(x)=\frac{x[x]}{1+x^2}$, where $[x]$ denotes the greatest integer $\le x$. Then the range of $f$ is :

Sets, Relations and Function

$\left(\frac35,\frac45\right)$$\left(\frac25,\frac45\right]$$\left(\frac25,\frac12\right)\cup\left(\frac35,\frac45\right]$$\left(\frac25,\frac35\right]\cup\left(\frac34,\frac45\right)$

JEE Main 2025 (Online) 3rd April Morning ShiftQuestion 34

Let $A=\{-3,-2,-1,0,1,2,3\}$. Let $R$ be a relation on $A$ defined by $xRy$ if and only if $0\le x^{2}+2y\le4$. 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

Sets, Relations and Function

$20$$17$$18$$19$

JEE Main 2022 (Online) 24th June Evening ShiftQuestion 35

Let $x*y=x^{2}+y^{3}$ and $(x*1)*1=x*(1*1)$. Then a value of $2\sin^{-1}\left(\frac{x^{4}+x^{2}-2}{x^{4}+x^{2}+2}\right)$ is

Sets, Relations and Function

$\frac{\pi}{4}$$\frac{\pi}{3}$$\frac{\pi}{2}$$\frac{\pi}{6}$

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