JEE Maths PYQ Practice, chapter-wise

JEE Main 2021 (Online) 4th August Evening ShiftQuestion 416

The distance of the point $(5,6,9)$ from the plane, which passes through the line of intersection of the planes $x+y-z=1$ and $2x+3y+4z=5$, and is perpendicular to the plane $x-y+z=0$ is

3D Geometry

$\sqrt{31}$$2\sqrt{31}$$\sqrt{62}$$2\sqrt{62}$

JEE Main 2021 (Online) 16th March Morning ShiftQuestion 417

Let $P$ be a plane $lx+my+nz=0$ containing the line, $\dfrac{1-x}{1}=\dfrac{y+4}{2}=\dfrac{z+2}{3}$. If plane $P$ divides the line segment $AB$ joining points $A(-3,-6,1)$ and $B(2,4,-3)$ in ratio $k:1$ then the value of $k$ is equal to :

3D Geometry

$2$$1.5$$3$$4$

JEE Main 2021 (Online) 16th March Morning ShiftQuestion 418

If for $a>0$, the feet of perpendiculars from the points $A(a,-2a,3)$ and $B(0,4,5)$ on the plane $lx+my+nz=0$ are points $C(0,-a,-1)$ and $D$ respectively, then the length of line segment $CD$ is equal to :

3D Geometry

$\sqrt{31}$$\sqrt{66}$$\sqrt{41}$$\sqrt{55}$

JEE Main 2021 (Online) 16th March Morning ShiftQuestion 419

Let the position vectors of two points $P$ and $Q$ be $3\hat{i}-\hat{j}+2\hat{k}$ and $\hat{i}+2\hat{j}-4\hat{k}$, respectively. Let $R$ and $S$ be two points such that the direction ratios of lines $PR$ and $QS$ are $(4,-1,2)$ and $(-2,1,-2)$, respectively. Let lines $PR$ and $QS$ intersect at $T$. If the vector $\overrightarrow{TA}$ is perpendicular to both $\overrightarrow{PR}$ and $\overrightarrow{QS}$ and the length of vector $\overrightarrow{TA}$ is $\sqrt{5}$ units, then the modulus of a position vector of $A$ is :

3D Geometry

$\sqrt{5}$$\sqrt{171}$$\sqrt{227}$$\sqrt{482}$

JEE Main 2024 (Online) 4th April Morning ShiftQuestion 420

Let the point, on the line passing through the points $P(1,-2,3)$ and $Q(5,-4,7)$, farther from the origin and at a distance of $9$ units from the point $P$, be $(\alpha,\beta,\gamma)$. Then $\alpha^{2}+\beta^{2}+\gamma^{2}$ is equal to :

3D Geometry

$150$$165$$160$$155$