JEE Maths PYQ Practice, chapter-wise

JEE Main 2018 (Online) 16th AprilQuestion 291

The sum of the intercepts on the coordinate axes of the plane passing through the point $(-2,-2,2)$ and containing the line joining the points $(1,-1,2)$ and $(1,1,1)$ is

3D Geometry

$4$$12$$-8$$-4$

JEE Advanced 2022 Paper 1Question 292

Let $P_1$ and $P_2$ be two planes given by $$P_1:\ 10x+15y+12z-60=0,$$ $$P_2:\ -2x+5y+4z-20=0.$$ Which of the following straight lines can be an edge of some tetrahedron whose two faces lie on $P_1$ and $P_2$ ?

3D Geometry

More than one option may be correct.

$\frac{x-1}{0}=\frac{y-1}{0}=\frac{z-1}{5}$$\frac{x-6}{-5}=\frac{y}{2}=\frac{z}{3}$$\frac{x}{-2}=\frac{y-4}{5}=\frac{z}{4}$$\frac{x}{1}=\frac{y-4}{-2}=\frac{z}{3}$

JEE Main 2019 (Online) 10th April Evening ShiftQuestion 293

A perpendicular is drawn from a point on the line $\frac{x-1}{2}=\frac{y+1}{-1}=\frac z1$ to the plane $x+y+z=3$ such that the foot of the perpendicular $Q$ also lies on the plane $x-y+z=3$. Then the coordinates of $Q$ are

3D Geometry

$(2,0,1)$$(-1,0,4)$$(4,0,-1)$$(1,0,2)$

JEE Main 2015 (Online) 10th AprilQuestion 294

If the shortest distance between the line $\frac{x-1}{\alpha}=\frac{y+1}{-1}=\frac z1$, $(\alpha\ne-1)$, and $x+y+z+1=0=2x-y+z+3$ is $\frac1{\sqrt3}$, then the value of $\alpha$ is :

3D Geometry

$-\frac{19}{16}$$\frac{32}{19}$$-\frac{16}{19}$$\frac{19}{32}$

JEE Main 2019 (Online) 10th April Morning ShiftQuestion 295

If the length of the perpendicular from the point $(\beta,0,\beta)$, ($\beta\neq0$) to the line $\frac x1=\frac{y-1}{0}=\frac{z+1}{-1}$ is $\sqrt{\frac32}$, then $\beta$ is equal to

3D Geometry

$2$$-1$$-2$$1$