JEE Maths PYQ Practice, chapter-wise

JEE Main 2023 (Online) 13th April Evening ShiftQuestion 81

The line, that is coplanar to the line $\frac{x+3}{-3}=\frac{y-1}{1}=\frac{z-5}{5}$, is

3D Geometry

$\frac{x-1}{-1}=\frac{y-2}{2}=\frac{z-5}{5}$$\frac{x+1}{-1}=\frac{y-2}{2}=\frac{z-5}{5}$$\frac{x+1}{-1}=\frac{y-2}{2}=\frac{z-5}{4}$$\frac{x+1}{1}=\frac{y-2}{2}=\frac{z-5}{5}$

JEE Main 2022 (Online) 25th June Morning ShiftQuestion 82

Let $Q$ be the mirror image of the point $P(1,0,1)$ with respect to the plane $S:x+y+z=5$. If a line $L$ passing through $(1,-1,-1)$, parallel to the line $PQ$ meets the plane $S$ at $R$, then $QR^{2}$ is equal to :

3D Geometry

$2$$5$$7$$11$

JEE Main 2025 (Online) 3rd April Evening ShiftQuestion 83

Each of the angles $\beta$ and $\gamma$ that a given line makes with the positive $y$- and $z$-axes, respectively, is half of the angle that this line makes with the positive $x$-axes. Then the sum of all possible values of the angle $\beta$ is

3D Geometry

$\pi$$\frac{3\pi}{2}$$\frac{3\pi}{4}$$\frac{\pi}{2}$

JEE Main 2024 (Online) 31st January Morning ShiftQuestion 84

The distance of the point $Q(0,2,-2)$ form the line passing through the point $P(5,-4,3)$ and perpendicular to the lines $\vec{r}=\left(-3\hat{i}+2\hat{k}\right)+\lambda\left(2\hat{i}+3\hat{j}+5\hat{k}\right)$, $\lambda\in\mathbb{R}$ and $\vec{r}=\left(\hat{i}-2\hat{j}+\hat{k}\right)+\mu\left(-\hat{i}+3\hat{j}+2\hat{k}\right)$, $\mu\in\mathbb{R}$ is

3D Geometry

$\sqrt{86}$$\sqrt{74}$$\sqrt{54}$$\sqrt{20}$

JEE Main 2022 (Online) 26th June Morning ShiftQuestion 85

If the two lines $l_1:\frac{x-2}{3}=\frac{y+1}{-2}$, $z=2$ and $l_2:\frac{x-1}{1}=\frac{2y+3}{\alpha}=\frac{z+5}{2}$ are perpendicular, then an angle between the lines $l_2$ and $l_3:\frac{1-x}{3}=\frac{2y-1}{-4}=\frac{z}{4}$ is :

3D Geometry

$\cos^{-1}\left(\frac{29}{4}\right)$$\sec^{-1}\left(\frac{29}{4}\right)$$\cos^{-1}\left(\frac{2}{29}\right)$$\cos^{-1}\left(\frac{2}{\sqrt{29}}\right)$