JEE Maths PYQ Practice, chapter-wise

JEE Advanced 2018 Paper 2Question 401

Let $P$ be a point in the first octant, whose image $Q$ in the plane $x+y=3$ (that is, the line segment $PQ$ is perpendicular to the plane $x+y=3$ and the mid-point of $PQ$ lies in the plane $x+y=3$) lies on the $z$-axis. Let the distance of $P$ from the $x$-axis be $5$. If $R$ is the image of $P$ in the $xy$-plane, then the length of $PR$ is _____ .

3D Geometry

Your answer

JEE Advanced 2020 Paper 2Question 402

Let $\alpha,\beta,\gamma,\delta$ be real numbers such that $\alpha^2+\beta^2+\gamma^2\neq0$ and $\alpha+\gamma=1$. Suppose the point $(3,2,-1)$ is the mirror image of the point $(1,0,-1)$ with respect to the plane $\alpha x+\beta y+\gamma z=\delta$. Then which of the following statements is/are TRUE?

3D Geometry

More than one option may be correct.

$\alpha+\beta=2$$\delta-\gamma=3$$\delta+\beta=4$$\alpha+\beta+\gamma=\delta$

JEE Advanced 2020 Paper 1Question 403

Let $L_1$ and $L_2$ be the following straight lines. $$L_1:\frac{x-1}{1}=\frac{y}{-1}=\frac{z-1}{3}\ \text{ and }\ L_2:\frac{x-1}{-3}=\frac{y}{-1}=\frac{z-1}{1}.$$ Suppose the straight line $$L:\frac{x-\alpha}{l}=\frac{y-1}{m}=\frac{z-\gamma}{-2}$$ lies in the plane containing $L_1$ and $L_2$, and passes through the point of intersection of $L_1$ and $L_2$. If the line $L$ bisects the acute angle between the lines $L_1$ and $L_2$, then which of the following statements is/are TRUE?

3D Geometry

More than one option may be correct.

$\alpha-\gamma=3$$l+m=2$$\alpha-\gamma=1$$l+m=0$

JEE Main 2025 (Online) 23rd January Evening ShiftQuestion 404

If the square of the shortest distance between the lines $\frac{x-2}{1}=\frac{y-1}{2}=\frac{z+3}{-3}$ and $\frac{x+1}{2}=\frac{y+3}{4}=\frac{z+5}{-5}$ is $\frac{m}{n}$, where $m,n$ are coprime numbers, then $m+n$ is equal to :

3D Geometry

$6$$9$$14$$21$

JEE Main 2025 (Online) 28th January Morning ShiftQuestion 405

If the image of the point $(4,4,3)$ in the line $\frac{x-1}{2}=\frac{y-2}{1}=\frac{z-1}{3}$ is $(\alpha,\beta,\gamma)$, then $\alpha+\beta+\gamma$ is equal to

3D Geometry

$7$$8$$9$$12$