JEE Maths PYQ Practice, chapter-wise

JEE Main 2025 (Online) 4th April Morning ShiftQuestion 41

Consider the sets $A=\{(x,y)\in\mathbb{R}\times\mathbb{R}:x^{2}+y^{2}=25\}$, $B=\{(x,y)\in\mathbb{R}\times\mathbb{R}:x^{2}+9y^{2}=144\}$, $C=\{(x,y)\in\mathbb{Z}\times\mathbb{Z}:x^{2}+y^{2}\le4\}$ and $D=A\cap B$. The total number of one-one functions from the set $D$ to the set $C$ is:

Sets, Relations and Function

$15120$$17160$$18290$$19320$

JEE Main 2025 (Online) 4th April Evening ShiftQuestion 42

Let $A=\{-3,-2,-1,0,1,2,3\}$ and $R$ be a relation on $A$ defined by $xRy$ if and only if $2x-y\in\{0,1\}$. Let $l$ be the number of elements in $R$. Let $m$ and $n$ be the minimum number of elements required to be added in $R$ to make it reflexive and symmetric relations, respectively. Then $l+m+n$ is equal to :

Sets, Relations and Function

$15$$16$$17$$18$

JEE Main 2020 (Online) 9th January Evening ShiftQuestion 43

Let $[t]$ denote the greatest integer $\le t$ and $\lim_{x\to0}x\left[\frac4x\right]=A$. Then the function, $f(x)=[x^2]\sin(\pi x)$ is discontinuous, when $x$ is equal to :

Sets, Relations and Function

$\sqrt A$$\sqrt{A+1}$$\sqrt{A+5}$$\sqrt{A+21}$

JEE Main 2025 (Online) 4th April Morning ShiftQuestion 44

Let $A=\{1,6,11,16,\ldots\}$ and $B=\{9,16,23,30,\ldots\}$ be the sets consisting of the first $2025$ terms of two arithmetic progressions. Then $n(A\cup B)$ is

Sets, Relations and Function

$3814$$3761$$4027$$4003$

JEE Main 2020 (Online) 8th January Morning ShiftQuestion 45

Let $f:\mathbf{R}\to\mathbf{R}$ be such that for all $x\in\mathbf{R}$, $(2^{1+x}+2^{1-x})$, $f(x)$ and $(3^x+3^{-x})$ are in A.P., then the minimum value of $f(x)$ is :

Sets, Relations and Function

$0$$2$$3$$4$

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