JEE Maths PYQ Practice, chapter-wise

JEE Main 2023 (Online) 24th January Evening ShiftQuestion 326

If the foot of the perpendicular drawn from $(1,9,7)$ to the line passing through the point $(3,2,1)$ and parallel to the planes $x+2y+z=0$ and $3y-z=3$ is $(\alpha,\beta,\gamma)$, then $\alpha+\beta+\gamma$ is equal to

3D Geometry

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

JEE Advanced 2024 Paper 2Question 327

A straight line drawn from the point $P(1,3,2)$, parallel to the line $\frac{x-2}{1}=\frac{y-4}{2}=\frac{z-6}{1}$, intersects the plane $L_1: x-y+3z=6$ at the point $Q$. Another straight line which passes through $Q$ and is perpendicular to the plane $L_1$ intersects the plane $L_2: 2x-y+z=-4$ at the point $R$. Then which of the following statements is (are) TRUE?

3D Geometry

More than one option may be correct.

The length of the line segment $PQ$ is $\sqrt6$The coordinates of $R$ are $(1,6,3)$The centroid of the triangle $PQR$ is $\left(\frac43,\frac{14}{3},\frac53\right)$The perimeter of the triangle $PQR$ is $\sqrt2+\sqrt6+\sqrt{11}$

JEE Main 2019 (Online) 12th January Evening ShiftQuestion 328

Let $S$ be the set of all real values of $\lambda$ such that a plane passing through the points $(-\lambda^{2},1,1)$, $(1,-\lambda^{2},1)$ and $(1,1,-\lambda^{2})$ also passes through the point $(-1,-1,1)$. Then $S$ is equal to :

3D Geometry

$\{\sqrt3\}$$\{3,-3\}$$\{1,-1\}$$\{\sqrt3,-\sqrt3\}$

JEE Main 2025 (Online) 29th January Morning ShiftQuestion 329

Let $L_1:\frac{x-1}{1}=\frac{y-2}{-1}=\frac{z-1}{2}$ and $L_2:\frac{x+1}{-1}=\frac{y-2}{2}=\frac z1$ be two lines. Let $L_3$ be a line passing through the point $(\alpha,\beta,\gamma)$ and be perpendicular to both $L_1$ and $L_2$. If $L_3$ intersects $L_1$, then $|5\alpha-11\beta-8\gamma|$ equals :

3D Geometry

$20$$18$$25$$16$

JEE Main 2023 (Online) 31st January Evening ShiftQuestion 330

Let the plane $P: 8x+\alpha_1y+\alpha_2z+12=0$ be parallel to the line $L:\frac{x+2}{2}=\frac{y-3}{3}=\frac{z+4}{5}$. If the intercept of $P$ on the $y$-axis is $1$, then the distance between $P$ and $L$ is

3D Geometry

$\sqrt{\frac27}$$\frac{6}{\sqrt{14}}$$\sqrt{\frac72}$$\sqrt{14}$