JEE Maths PYQ Practice, chapter-wise

JEE Main 2021 (Online) 26th August Evening ShiftQuestion 26

A hall has a square floor of dimension $10\text{ m}\times10\text{ m}$ (see the figure) and vertical walls. If the angle $GPH$ between the diagonals $AG$ and $BH$ is $\cos^{-1}\frac{1}{5}$, then the height of the hall (in meters) is : [FIGURE NOT TRANSCRIBED: cuboid with vertices $A,B,C,D,E,F,G,H$, base $10\text{ m}\times10\text{ m}$, diagonals $AG$ and $BH$ meeting at $P$; see the paper image]

3D Geometry

$5\sqrt{2}$$5\sqrt{3}$$5$$2\sqrt{10}$

JEE Main 2021 (Online) 22nd July Evening ShiftQuestion 27

If the shortest distance between the straight lines $3(x-1)=6(y-2)=2(z-1)$ and $4(x-2)=2(y-\lambda)=(z-3)$, $\lambda\in\mathbf{R}$ is $\frac{1}{\sqrt{38}}$, then the integral value of $\lambda$ is equal to :

3D Geometry

$-1$$2$$3$$5$

JEE Main 2021 (Online) 27th August Morning ShiftQuestion 28

Equation of a plane at a distance $\sqrt{\frac{2}{21}}$ from the origin, which contains the line of intersection of the planes $x-y-z-1=0$ and $2x+y-3z+4=0$, is :

3D Geometry

$3x-4z+3=0$$-x+2y+2z-3=0$$3x-y-5z+2=0$$4x-y-5z+2=0$

JEE Main 2021 (Online) 31st August Morning ShiftQuestion 29

Let the equation of the plane, that passes through the point $(1,4,-3)$ and contains the line of intersection of the planes $3x-2y+4z-7=0$ and $x+5y-2z+9=0$, be $\alpha x+\beta y+\gamma z+3=0$, then $\alpha+\beta+\gamma$ is equal to :

3D Geometry

$23$$15$$-15$$-23$

JEE Main 2023 (Online) 12th April Morning ShiftQuestion 30

Let the lines $l_1:\frac{x+5}{3}=\frac{y+4}{1}=\frac{z-\alpha}{-2}$ and $l_2:3x+2y+z-2=0=x-3y+2z-13$ be coplanar. If the point $P(a,b,c)$ on $l_1$ is nearest to the point $Q(-4,-3,2)$, then $|a|+|b|+|c|$ is equal to

3D Geometry

$8$$10$$12$$14$