JEE Maths PYQ Practice, chapter-wise

JEE Main 2021 (Online) 3rd August Evening ShiftQuestion 36

Let $\mathbb{R}$ be the set of real numbers and '$*$' be a binary operation on $\mathbb{R}-\{0\}$ defined by $a*b=a+2b+\frac{a}{b}$. Then the operation '$*$' is

Sets, Relations and Function

associative and commutativecommutative but not associativeassociative but not commutativeneither associative nor commutative.

JEE Main 2020 (Online) 2nd September Morning ShiftQuestion 37

If $R=\{(x,y):x,y\in\mathbf{Z},x^2+3y^2\le8\}$ is a relation on the set of integers $\mathbf{Z}$, then the domain of $R^{-1}$ is :

Sets, Relations and Function

$\{-2,-1,0,1,2\}$$\{-2,-1,1,2\}$$\{-1,0,1\}$$\{0,1\}$

JEE Main 2022 (Online) 27th July Morning ShiftQuestion 38

Let $R_1$ and $R_2$ be two relations defined on $\mathbb{R}$ by $aR_1b\Leftrightarrow ab\ge0$ and $aR_2b\Leftrightarrow a\ge b$. Then,

Sets, Relations and Function

$R_1$ is an equivalence relation but not $R_2$$R_2$ is an equivalence relation but not $R_1$both $R_1$ and $R_2$ are equivalence relationsneither $R_1$ nor $R_2$ is an equivalence relation

JEE Main 2022 (Online) 28th July Evening ShiftQuestion 39

Let $S=\left\{x\in[-6,3]-\{-2,2\}:\frac{|x+3|-1}{|x|-2}\ge0\right\}$ and $T=\{x\in\mathbb{Z}:x^2-7|x|+9\le0\}$. Then the number of elements in $S\cap T$ is :

Sets, Relations and Function

$7$$5$$4$$3$

JEE Main 2022 (Online) 28th July Morning ShiftQuestion 40

For $\alpha\in\mathbf{N}$, consider a relation $R$ on $\mathbf{N}$ 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 :

Sets, Relations and Function

$\alpha=14$$\alpha$ is a multiple of $4$$4$ is the remainder when $\alpha$ is divided by $10$$4$ is the remainder when $\alpha$ is divided by $7$

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