JEE Maths PYQ Practice, chapter-wise

JEE Main 2023 (Online) 25th January Morning ShiftQuestion 306

Consider the lines $L_1$ and $L_2$ given by $L_1:\frac{x-1}{2}=\frac{y-3}{1}=\frac{z-2}{2}$ $L_2:\frac{x-2}{1}=\frac{y-2}{2}=\frac{z-3}{3}$ A line $L_3$ having direction ratios $1,-1,-2$, intersects $L_1$ and $L_2$ at the points $P$ and $Q$ respectively. Then the length of line segment $PQ$ is

3D Geometry

$2\sqrt6$$3\sqrt2$$4\sqrt3$$4$

JEE Main 2023 (Online) 25th January Evening ShiftQuestion 307

The shortest distance between the lines $x+1=2y=-12z$ and $x=y+2=6z-6$ is :

3D Geometry

$2$$3$$\frac52$$\frac32$

JEE Main 2023 (Online) 30th January Morning ShiftQuestion 308

The line $l_1$ passes through the point $(2,6,2)$ and is perpendicular to the plane $2x+y-2z=10$. Then the shortest distance between the line $l_1$ and the line $\frac{x+1}{2}=\frac{y+4}{-3}=\frac z2$ is:

3D Geometry

$7$$\frac{19}3$$\frac{19}2$$9$

JEE Main 2024 (Online) 27th January Evening ShiftQuestion 309

Let the image of the point $(1,0,7)$ in the line $\frac x1=\frac{y-1}{2}=\frac{z-2}{3}$ be the point $(\alpha,\beta,\gamma)$. Then which one of the following points lies on the line passing through $(\alpha,\beta,\gamma)$ and making angles $\frac{2\pi}{3}$ and $\frac{3\pi}{4}$ with $y$-axis and $z$-axis respectively and an acute angle with $x$-axis?

3D Geometry

$\left(1,-2,1+\sqrt2\right)$$\left(1,2,1-\sqrt2\right)$$\left(3,4,3-2\sqrt2\right)$$\left(3,-4,3+2\sqrt2\right)$

JEE Main 2025 (Online) 24th January Morning ShiftQuestion 310

Let in a $\triangle ABC$, the length of the side $AC$ be $6$, the vertex $B$ be $(1,2,3)$ and the vertices $A,C$ lie on the line $\frac{x-6}{3}=\frac{y-7}{2}=\frac{z-7}{-2}$. Then the area (in sq. units) of $\triangle ABC$ is :

3D Geometry

$17$$21$$56$$42$