JEE Maths PYQ Practice, chapter-wise

JEE Main 2023 (Online) 1st February Evening ShiftQuestion 311

Let the plane $P$ pass through the intersection of the planes $2x+3y-z=2$ and $x+2y+3z=6$, and be perpendicular to the plane $2x+y-z+1=0$. If $d$ is the distance of $P$ from the point $(-7,1,1)$, then $d^{2}$ is equal to :

3D Geometry

$\frac{250}{83}$$\frac{15}{53}$$\frac{25}{83}$$\frac{250}{82}$

JEE Main 2023 (Online) 30th January Morning ShiftQuestion 312

Let a unit vector $\overrightarrow{OP}$ make angles $\alpha,\beta,\gamma$ with the positive directions of the co-ordinate axes $OX,OY,OZ$ respectively, where $\beta\in\left[0,\frac\pi2\right]$. If $\overrightarrow{OP}$ is perpendicular to the plane through points $(1,2,3)$, $(2,3,4)$ and $(1,5,7)$, then which one of the following is true ?

3D Geometry

$\alpha\in\left(\frac\pi2,\pi\right)$ and $\gamma\in\left(\frac\pi2,\pi\right)$$\alpha\in\left(0,\frac\pi2\right)$ and $\gamma\in\left(0,\frac\pi2\right)$$\alpha\in\left(\frac\pi2,\pi\right)$ and $\gamma\in\left(0,\frac\pi2\right)$$\alpha\in\left(0,\frac\pi2\right)$ and $\gamma\in\left(\frac\pi2,\pi\right)$

JEE Main 2023 (Online) 31st January Evening ShiftQuestion 313

Let $P$ be the plane, passing through the point $(1,-1,-5)$ and perpendicular to the line joining the points $(4,1,-3)$ and $(2,4,3)$. Then the distance of $P$ from the point $(3,-2,2)$ is

3D Geometry

$6$$4$$5$$7$

JEE Main 2023 (Online) 1st February Morning ShiftQuestion 314

The shortest distance between the lines $\frac{x-5}{1}=\frac{y-2}{2}=\frac{z-4}{-3}$ and $\frac{x+3}{1}=\frac{y+5}{4}=\frac{z-1}{-5}$ is

3D Geometry

$7\sqrt3$$5\sqrt3$$6\sqrt3$$4\sqrt3$

JEE Main 2023 (Online) 1st February Morning ShiftQuestion 315

Let the image of the point $P(2,-1,3)$ in the plane $x+2y-z=0$ be $Q$. Then the distance of the plane $3x+2y+z+29=0$ from the point $Q$ is

3D Geometry

$\frac{22\sqrt2}{7}$$\frac{24\sqrt2}{7}$$2\sqrt{14}$$3\sqrt{14}$