JEE Maths PYQ Practice, chapter-wise

JEE Main 2025 (Online) 7th April Evening ShiftQuestion 11

Let $A=\{(\alpha,\beta)\in\mathbb{R}\times\mathbb{R}:|\alpha-1|\le4\text{ and }|\beta-5|\le6\}$ and $B=\{(\alpha,\beta)\in\mathbb{R}\times\mathbb{R}:16(\alpha-2)^{2}+9(\beta-6)^{2}\le144\}$. Then

Sets, Relations and Function

$A\subset B$$B\subset A$$A\cup B=\{(x,y):-4\le x\le4,\ -1\le y\le11\}$neither $A\subset B$ nor $B\subset A$

JEE Main 2022 (Online) 27th July Morning ShiftQuestion 12

Let $f,g:\mathbb{N}-\{1\}\to\mathbb{N}$ be functions defined by $f(a)=\alpha$, where $\alpha$ is the maximum of the powers of those primes $p$ such that $p^\alpha$ divides $a$, and $g(a)=a+1$, for all $a\in\mathbb{N}-\{1\}$. Then, the function $f+g$ is

Sets, Relations and Function

one-one but not ontoonto but not one-oneboth one-one and ontoneither one-one nor onto

JEE Main 2022 (Online) 28th June Evening ShiftQuestion 13

Let $R_1=\{(a,b)\in\mathbf{N}\times\mathbf{N}:|a-b|\le13\}$ and $R_2=\{(a,b)\in\mathbf{N}\times\mathbf{N}:|a-b|\neq13\}$. Then on $\mathbf{N}$ :

Sets, Relations and Function

Both $R_1$ and $R_2$ are equivalence relationsNeither $R_1$ nor $R_2$ is an equivalence relation$R_1$ is an equivalence relation but $R_2$ is not$R_2$ is an equivalence relation but $R_1$ is not

JEE Main 2022 (Online) 25th July Morning ShiftQuestion 14

The total number of functions, $f:\{1,2,3,4\}\to\{1,2,3,4,5,6\}$ such that $f(1)+f(2)=f(3)$, is equal to :

Sets, Relations and Function

$60$$90$$108$$126$

JEE Main 2022 (Online) 28th July Morning ShiftQuestion 15

Let $\alpha,\beta$ and $\gamma$ be three positive real numbers. Let $f(x)=\alpha x^5+\beta x^3+\gamma x$, $x\in\mathbf{R}$ and $g:\mathbf{R}\to\mathbf{R}$ be such that $g(f(x))=x$ for all $x\in\mathbf{R}$. If $a_1,a_2,a_3,\ldots,a_n$ be in arithmetic progression with mean zero, then the value of $f\left(g\left(\frac1n\sum_{i=1}^{n}f(a_i)\right)\right)$ is equal to :

Sets, Relations and Function

$0$$3$$9$$27$

Question Bank