JEE Maths PYQ Practice, chapter-wise

JEE Advanced 2023 Paper 1Question 261

Let $Q$ be the cube with the set of vertices $\{(x_1,x_2,x_3)\in\mathbb{R}^3: x_1,x_2,x_3\in\{0,1\}\}$. Let $F$ be the set of all twelve lines containing the diagonals of the six faces of the cube $Q$. Let $S$ be the set of all four lines containing the main diagonals of the cube $Q$; for instance, the line passing through the vertices $(0,0,0)$ and $(1,1,1)$ is in $S$. For lines $\ell_1$ and $\ell_2$, let $d(\ell_1,\ell_2)$ denote the shortest distance between them. Then the maximum value of $d(\ell_1,\ell_2)$, as $\ell_1$ varies over $F$ and $\ell_2$ varies over $S$, is

3D Geometry

$\frac{1}{\sqrt6}$$\frac{1}{\sqrt8}$$\frac{1}{\sqrt3}$$\frac{1}{\sqrt{12}}$

JEE Main 2015 (Online) 11th AprilQuestion 262

The shortest distance between the $z$-axis and the line $x+y+2z-3=0=2x+3y+4z-4$, is

3D Geometry

$1$$2$$3$$4$

JEE Main 2018 (Online) 15th April Morning ShiftQuestion 263

A variable plane passes through a fixed point $(3,2,1)$ and meets $x$, $y$ and $z$ axes at $A$, $B$ and $C$ respectively. A plane is drawn parallel to $yz$-plane through $A$, a second plane is drawn parallel to $zx$ plane through $B$ and a third plane is drawn parallel to $xy$-plane through $C$. Then the locus of the point of intersection of these three planes, is

3D Geometry

$x+y+z=6$$\frac x3+\frac y2+\frac z1=1$$\frac3x+\frac2y+\frac1z=1$$\frac1x+\frac1y+\frac1z=\frac{11}6$

JEE Main 2018 (Offline)Question 264

If $L_1$ is the line of intersection of the planes $2x-2y+3z-2=0$, $x-y+z+1=0$ and $L_2$ is the line of intersection of the planes $x+2y-z-3=0$, $3x-y+2z-1=0$, then the distance of the origin from the plane, containing the lines $L_1$ and $L_2$ is

3D Geometry

$\frac1{\sqrt2}$$\frac1{4\sqrt2}$$\frac1{3\sqrt2}$$\frac1{2\sqrt2}$

JEE Main 2015 (Online) 10th AprilQuestion 265

If the points $(1,1,\lambda)$ and $(-3,0,1)$ are equidistant from the plane $3x+4y-12z+13=0$, then $\lambda$ satisfies the equation:

3D Geometry

$3x^2+10x+7=0$$3x^2+10x-13=0$$3x^2-10x+7=0$$3x^2-10x+21=0$