JEE Maths PYQ Practice, chapter-wise

JEE Advanced 2013 Paper 2Question 381

Consider the lines $L_1:\frac{x-1}{2}=\frac{y}{-1}=\frac{z+3}{1}$, $L_2:\frac{x-4}{1}=\frac{y+3}{1}=\frac{z+3}{2}$ and the planes $P_1: 7x+y+2z=3$, $P_2: 3x+5y-6z=4$. Let $ax+by+cz=d$ be the equation of the plane passing through the point of intersection of lines $L_1$ and $L_2$, and perpendicular to planes $P_1$ and $P_2$. Match List-I with List-II and select the correct answer using the code given below the lists: List I: P. $a=$ ; Q. $b=$ ; R. $c=$ ; S. $d=$ List II: 1. $13$ ; 2. $-3$ ; 3. $1$ ; 4. $-2$

3D Geometry

P-3, Q-2, R-4, S-1P-1, Q-3, R-4, S-2P-3, Q-2, R-1, S-4P-2, Q-4, R-1, S-3

JEE Advanced 2016 Paper 2Question 382

Let $P$ be the image of the point $(3,1,7)$ with respect to the plane $x-y+z=3$. Then the equation of the plane passing through $P$ and containing the straight line $\frac{x}{1}=\frac{y}{2}=\frac{z}{1}$ is

3D Geometry

$x+y-3z=0$$3x+z=0$$x-4y+7z=0$$2x-y=0$

AIEEE 2006 (Offline)Question 383

The two lines $x=ay+b$, $z=cy+d$; and $x=a'y+b'$, $z=c'y+d'$ are perpendicular to each other if :

3D Geometry

$aa'+cc'=-1$$aa'+cc'=1$$\frac{a}{a'}+\frac{c}{c'}=-1$$\frac{a}{a'}+\frac{c}{c'}=1$

AIEEE 2003 (Offline)Question 384

The two lines $x=ay+b$, $z=cy+d$ and $x=a'y+b'$, $z=c'y+d'$ will be perpendicular, if and only if :

3D Geometry

$aa'+cc'+1=0$$aa'+bb'cc'+1=0$$aa'+bb'cc'=0$$(a+a')(b+b')+(c+c')=0$

JEE Main 2014 (Online) 12th AprilQuestion 385

If the distance between planes $4x-2y-4z+1=0$ and $4x-2y-4z+d=0$ is $7$, then $d$ is :

3D Geometry

$41$ or $-42$$42$ or $-43$$-41$ or $43$$-42$ or $44$