JEE Maths PYQ Practice, chapter-wise

IIT-JEE 2006Question 356

A plane passes through $(1,-2,1)$ and is perpendicular to two planes $2x-2y+z=0$ and $x-y+2z=4$. The distance of the plane from the point $(1,2,2)$ is

3D Geometry

$0$$1$$\sqrt2$$2\sqrt2$

IIT-JEE 2005 ScreeningQuestion 357

A variable plane at a distance of one unit from the origin cuts the coordinate axes at $A,B$ and $C$. If the centroid $D(x,y,z)$ of triangle $ABC$ satisfies the relation $\dfrac1{x^{2}}+\dfrac1{y^{2}}+\dfrac1{z^{2}}=k$, then the value of $k$ is

3D Geometry

$3$$1$$\dfrac13$$9$

JEE Main 2026 (Online) 23rd January Morning ShiftQuestion 358

The vertices $B$ and $C$ of a triangle $ABC$ lie on the line $\frac{x}{1}=\frac{1-y}{-2}=\frac{z-2}{3}$. The coordinates of $A$ and $B$ are $(1,6,3)$ and $(4,9,\alpha)$ respectively and $C$ is at a distance of $10$ units from $B$. The area (in sq. units) of $\triangle ABC$ is :

3D Geometry

$15\sqrt{13}$$20\sqrt{13}$$5\sqrt{13}$$10\sqrt{13}$

JEE Main 2026 (Online) 22nd January Morning ShiftQuestion 359

Let $P(\alpha,\beta,\gamma)$ be the point on the line $\frac{x-1}{2}=\frac{y+1}{-3}=z$ at a distance $4\sqrt{14}$ from the point $(1,-1,0)$ and nearer to the origin. Then the shortest distance between the lines $\frac{x-\alpha}{1}=\frac{y-\beta}{2}=\frac{z-\gamma}{3}$ and $\frac{x+5}{2}=\frac{y-10}{1}=\frac{z-3}{1}$, is equal to :

3D Geometry

$4\sqrt{\frac75}$$4\sqrt{\frac57}$$7\sqrt{\frac54}$$2\sqrt{\frac74}$

JEE Main 2026 (Online) 23rd January Evening ShiftQuestion 360

If the image of the point $P(a,2,a)$ in the line $\frac x2=\frac{y+a}{1}=\frac z1$ is $Q$ and the image of $Q$ in the line $\frac{x-2b}{2}=\frac{y-a}{1}=\frac{z+2b}{-5}$ is $P$, then $a+b$ is equal to $\_\_\_\_\_\_$ .

3D Geometry

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