JEE Maths PYQ Practice, chapter-wise

JEE Main 2020 (Online) 9th January Evening ShiftQuestion 1

If $A=\{x\in\mathbf{R}:|x|<2\}$ and $B=\{x\in\mathbf{R}:|x-2|\ge3\}$; then :

Sets, Relations and Function

$A-B=[-1,2)$$B-A=\mathbf{R}-(-2,5)$$A\cap B=(-2,-1)$$A\cup B=\mathbf{R}-(2,5)$

JEE Main 2024 (Online) 29th January Morning ShiftQuestion 2

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

Sets, Relations and Function

Reflexive and transitive but not symmetricReflexive and symmetric but not transitiveReflexive, symmetric and transitiveReflexive but neither symmetric nor transitive

JEE Main 2024 (Online) 6th April Morning ShiftQuestion 3

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 $N$ be the minimum number of elements required to be added in $R_1$ and $R_2$, respectively, in order to make the relations symmetric, then $M+N$ equals

Sets, Relations and Function

$8$$10$$12$$16$

JEE Main 2021 (Online) 18th March Evening ShiftQuestion 4

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 ?

Sets, Relations and Function

$R$ is reflexive, symmetric but not transitive$R$ is reflexive, transitive but not symmetric$R$ is symmetric, transitive but not reflexive,$R$ is an equivalence relation

JEE Main 2023 (Online) 6th April Morning ShiftQuestion 5

Let $A=\{x\in\mathbb{R}:[x+3]+[x+4]\le3\}$, $B=\left\{x\in\mathbb{R}:3^{x}\left(\sum_{r=1}^{\infty}\frac{3}{10^{r}}\right)^{x-3}<3^{-3x}\right\}$, where $[t]$ denotes greatest integer function. Then,

Sets, Relations and Function

$A=B$$A\subset B,\ A\neq B$$B\subset C,\ A\neq B$$A\cap B=\phi$