JEE Maths PYQ Practice, chapter-wise

JEE Main 2025 (Online) 22nd January Morning ShiftQuestion 431

Let $L_1:\dfrac{x-1}{2}=\dfrac{y-2}{3}=\dfrac{z-3}{4}$ and $L_2:\dfrac{x-2}{3}=\dfrac{y-4}{4}=\dfrac{z-5}{5}$ be two lines. Then which of the following points lies on the line of the shortest distance between $L_1$ and $L_2$?

3D Geometry

$\left(\dfrac{14}{3},-3,\dfrac{22}{3}\right)$$\left(2,3,\dfrac{1}{3}\right)$$\left(\dfrac{8}{3},-1,\dfrac{1}{3}\right)$$\left(-\dfrac{5}{3},-7,1\right)$

JEE Main 2025 (Online) 22nd January Evening ShiftQuestion 432

The perpendicular distance, of the line $\dfrac{x-1}{2}=\dfrac{y+2}{-1}=\dfrac{z+3}{2}$ from the point $P(2,-10,1)$, is :

3D Geometry

$6$$4\sqrt{3}$$3\sqrt{5}$$5\sqrt{2}$

JEE Main 2025 (Online) 22nd January Evening ShiftQuestion 433

Let a line pass through two distinct points $P(-2,-1,3)$ and $Q$, and be parallel to the vector $3\hat{i}+2\hat{j}+2\hat{k}$. If the distance of the point $Q$ from the point $R(1,3,3)$ is $5$, then the square of the area of $\triangle PQR$ is equal to :

3D Geometry

$148$$144$$136$$140$

JEE Main 2025 (Online) 23rd January Morning ShiftQuestion 434

Let the position vectors of the vertices $A$, $B$ and $C$ of a tetrahedron $ABCD$ be $\hat{i}+2\hat{j}+\hat{k}$, $\hat{i}+3\hat{j}-2\hat{k}$ and $2\hat{i}+\hat{j}-\hat{k}$ respectively. The altitude from the vertex $D$ to the opposite face $ABC$ meets the median line segment through $A$ of the triangle $ABC$ at the point $E$. If the length of $AD$ is $\dfrac{\sqrt{110}}{3}$ and the volume of the tetrahedron is $\dfrac{\sqrt{805}}{6\sqrt{2}}$, then the position vector of $E$ is

3D Geometry

$\dfrac{1}{6}\left(7\hat{i}+12\hat{j}+\hat{k}\right)$$\dfrac{1}{12}\left(7\hat{i}+4\hat{j}+3\hat{k}\right)$$\dfrac{1}{6}\left(12\hat{i}+12\hat{j}+\hat{k}\right)$$\dfrac{1}{2}\left(\hat{i}+4\hat{j}+7\hat{k}\right)$

JEE Main 2025 (Online) 23rd January Morning ShiftQuestion 435

Let $P$ be the foot of the perpendicular from the point $Q(10,-3,-1)$ on the line $\dfrac{x-3}{7}=\dfrac{y-2}{-1}=\dfrac{z+1}{-2}$. Then the area of the right angled triangle $PQR$, where $R$ is the point $(3,-2,1)$, is

3D Geometry

$\sqrt{30}$$9\sqrt{15}$$3\sqrt{30}$$8\sqrt{15}$