JEE Maths PYQ Practice, chapter-wise

JEE Main 2025 (Online) 4th April Morning ShiftQuestion 101

Let $A$ and $B$ be two distinct points on the line $L:\frac{x-6}{3}=\frac{y-7}{2}=\frac{z-7}{-2}$. Both $A$ and $B$ are at a distance $2\sqrt{17}$ from the foot of perpendicular drawn from the point $(1,2,3)$ on the line $L$. If $O$ is the origin, then $\overrightarrow{OA}\cdot\overrightarrow{OB}$ is equal to

3D Geometry

$21$$47$$49$$62$

JEE Main 2024 (Online) 27th January Morning ShiftQuestion 102

If the shortest distance between the lines $\frac{x-4}{1}=\frac{y+1}{2}=\frac{z}{-3}$ and $\frac{x-\lambda}{2}=\frac{y+1}{4}=\frac{z-2}{-5}$ is $\frac{6}{\sqrt{5}}$, then the sum of all possible values of $\lambda$ is :

3D Geometry

$5$$7$$8$$10$

JEE Main 2022 (Online) 25th June Evening ShiftQuestion 103

Let $P$ be the plane passing through the intersection of the planes $\vec{r}\cdot\left(\hat{i}+3\hat{j}-\hat{k}\right)=5$ and $\vec{r}\cdot\left(2\hat{i}-\hat{j}+\hat{k}\right)=3$, and the point $(2,1,-2)$. Let the position vectors of the points $X$ and $Y$ be $\hat{i}-2\hat{j}+4\hat{k}$ and $5\hat{i}-\hat{j}+2\hat{k}$ respectively. Then the points

3D Geometry

$X$ and $X+Y$ are on the same side of $P$$Y$ and $Y-X$ are on the opposite sides of $P$$X$ and $Y$ are on the opposite sides of $P$$X+Y$ and $X-Y$ are on the same side of $P$

JEE Main 2024 (Online) 8th April Morning ShiftQuestion 104

If the shortest distance between the lines $L_1:\vec{r}=(2+\lambda)\hat{i}+(1-3\lambda)\hat{j}+(3+4\lambda)\hat{k}$, $\lambda\in\mathbb{R}$ $L_2:\vec{r}=2(1+\mu)\hat{i}+3(1+\mu)\hat{j}+(5+\mu)\hat{k}$, $\mu\in\mathbb{R}$ is $\frac{m}{\sqrt{n}}$, where $\gcd(m,n)=1$, then the value of $m+n$ equals

3D Geometry

$377$$384$$390$$387$

JEE Main 2024 (Online) 1st February Evening ShiftQuestion 105

If the mirror image of the point $P(3,4,9)$ in the line $\frac{x-1}{3}=\frac{y+1}{2}=\frac{z-2}{1}$ is $(\alpha,\beta,\gamma)$, then $14(\alpha+\beta+\gamma)$ is :

3D Geometry

$102$$108$$132$$138$