JEE Maths PYQ Practice, chapter-wise

JEE Advanced 2015 Paper 1Question 396

In $\mathbb{R}^3$, let $L$ be a straight line passing through the origin. Suppose that all the points on $L$ are at a constant distance from the two planes $P_1: x+2y-z+1=0$ and $P_2: 2x-y+z-1=0$. Let $M$ be the locus of the feet of the perpendiculars drawn from the points on $L$ to the plane $P_1$. Which of the following points lie(s) on $M$?

3D Geometry

More than one option may be correct.

$\left(0,-\frac56,-\frac23\right)$$\left(-\frac16,-\frac13,\frac16\right)$$\left(-\frac56,0,\frac16\right)$$\left(-\frac13,0,\frac23\right)$

JEE Advanced 2015 Paper 1Question 397

In $\mathbb{R}^3$, consider the planes $P_1: y=0$ and $P_2: x+z=1$. Let $P_3$ be a plane, different from $P_1$ and $P_2$, which passes through the intersection of $P_1$ and $P_2$. If the distance of the point $(0,1,0)$ from $P_3$ is 1 and the distance of a point $(\alpha,\beta,\gamma)$ from $P_3$ is 2, then which of the following relations is (are) true?

3D Geometry

More than one option may be correct.

$2\alpha+\beta+2\gamma+2=0$$2\alpha-\beta+2\gamma+4=0$$2\alpha+\beta-2\gamma-10=0$$2\alpha-\beta+2\gamma-8=0$

JEE Advanced 2016 Paper 1Question 398

Consider a pyramid $OPQRS$ located in the first octant ($x\ge0,y\ge0,z\ge0$) with $O$ as origin, and $OP$ and $OR$ along the $x$-axis and the $y$-axis, respectively. The base $OPQR$ of the pyramid is a square with $OP=3$. The point $S$ is directly above the mid-point $T$ of diagonal $OQ$ such that $TS=3$. Then

3D Geometry

More than one option may be correct.

the acute angle between $OQ$ and $OS$ is $\frac{\pi}{3}$the equation of the plane containing the triangle $OQS$ is $x-y=0$the length of the perpendicular from $P$ to the plane containing the triangle $OQS$ is $\frac{3}{\sqrt{2}}$the perpendicular distance from $O$ to the straight line containing $RS$ is $\sqrt{\frac{15}{2}}$

JEE Advanced 2017 Paper 2Question 399

The equation of the plane passing through the point $(1, 1, 1)$ and perpendicular to the planes $2x + y - 2z = 5$ and $3x - 6y - 2z = 7$, is

3D Geometry

$14x + 2y - 15z = 1$$14x - 2y + 15z = 27$$14x + 2y + 15z = 31$$-14x + 2y + 15z = 3$

JEE Advanced 2018 Paper 1Question 400

Let $P_1: 2x+y-z=3$ and $P_2: x+2y+z=2$ be two planes. Then, which of the following statement(s) is (are) TRUE?

3D Geometry

More than one option may be correct.

The line of intersection of $P_1$ and $P_2$ has direction ratios $1,2,-1$The line $$\frac{3x-4}{9}=\frac{1-3y}{9}=\frac{z}{3}$$ is perpendicular to the line of intersection of $P_1$ and $P_2$The acute angle between $P_1$ and $P_2$ is $60^\circ$If $P_3$ is the plane passing through the point $(4,2,-2)$ and perpendicular to the line of intersection of $P_1$ and $P_2$, then the distance of the point $(2,1,1)$ from the plane $P_3$ is $\frac{2}{\sqrt{3}}$