JEE Maths PYQ Practice, chapter-wise

JEE Main 2025 (Online) 3rd April Morning ShiftQuestion 76

Line $L_1$ passes through the point $(1,2,3)$ and is parallel to $z$-axis. Line $L_2$ passes through the point $(\lambda,5,6)$ and is parallel to $y$-axis. Let for $\lambda=\lambda_1,\lambda_2$, $\lambda_2<\lambda_1$, the shortest distance between the two lines be $3$. Then the square of the distance of the point $(\lambda_1,\lambda_2,7)$ from the line $L_1$ is

3D Geometry

$25$$32$$37$$40$

JEE Main 2023 (Online) 15th April Morning ShiftQuestion 77

Let the foot of perpendicular of the point $P(3,-2,-9)$ on the plane passing through the points $(-1,-2,-3)$, $(9,3,4)$, $(9,-2,1)$ be $Q(\alpha,\beta,\gamma)$. Then the distance of $Q$ from the origin is

3D Geometry

$\sqrt{35}$$\sqrt{38}$$\sqrt{29}$$\sqrt{42}$

JEE Main 2022 (Online) 24th June Evening ShiftQuestion 78

Let the points on the plane $P$ be equidistant from the points $(-4,2,1)$ and $(2,-2,3)$. Then the acute angle between the plane $P$ and the plane $2x+y+3z=1$ is

3D Geometry

$\frac{\pi}{6}$$\frac{\pi}{4}$$\frac{\pi}{3}$$\frac{5\pi}{12}$

JEE Main 2025 (Online) 3rd April Morning ShiftQuestion 79

Let a line passing through the point $(4,1,0)$ intersect the line $L_1:\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ at the point $A(\alpha,\beta,\gamma)$ and the line $L_2:x-6=y=-z+4$ at the point $B(a,b,c)$. Then $\begin{vmatrix}1&0&1\\\alpha&\beta&\gamma\\a&b&c\end{vmatrix}$ is equal to

3D Geometry

$8$$6$$12$$16$

JEE Main 2024 (Online) 8th April Morning ShiftQuestion 80

Let $P(x,y,z)$ be a point in the first octant, whose projection in the $xy$-plane is the point $Q$. Let $OP=\gamma$; the angle between $OQ$ and the positive $x$-axis be $\theta$; and the angle between $OP$ and the positive $z$-axis be $\phi$, where $O$ is the origin. Then the distance of $P$ from the $x$-axis is

3D Geometry

$\gamma\sqrt{1-\sin^{2}\phi\cos^{2}\theta}$$\gamma\sqrt{1-\sin^{2}\theta\cos^{2}\phi}$$\gamma\sqrt{1+\cos^{2}\theta\sin^{2}\phi}$$\gamma\sqrt{1+\cos^{2}\phi\sin^{2}\theta}$