JEE Maths PYQ Practice, chapter-wise

JEE Main 2024 (Online) 30th January Evening ShiftQuestion 71

Let $L_1:\vec{r}=\left(\hat{i}-\hat{j}+2\hat{k}\right)+\lambda\left(\hat{i}-\hat{j}+2\hat{k}\right)$, $\lambda\in\mathbb{R}$, $L_2:\vec{r}=\left(\hat{j}-\hat{k}\right)+\mu\left(3\hat{i}+\hat{j}+p\hat{k}\right)$, $\mu\in\mathbb{R}$ and $L_3:\vec{r}=\delta\left(\ell\hat{i}+m\hat{j}+n\hat{k}\right)$, $\delta\in\mathbb{R}$ be three lines such that $L_1$ is perpendicular to $L_2$ and $L_3$ is perpendicular to both $L_1$ and $L_2$. Then, the point which lies on $L_3$ is

3D Geometry

$(1,7,-4)$$(-1,7,4)$$(1,-7,4)$$(-1,-7,4)$

JEE Main 2024 (Online) 29th January Morning ShiftQuestion 72

Let $PQR$ be a triangle with $R(-1,4,2)$. Suppose $M(2,1,2)$ is the mid point of $PQ$. The distance of the centroid of $\triangle PQR$ from the point of intersection of the lines $\frac{x-2}{0}=\frac{y}{2}=\frac{z+3}{-1}$ and $\frac{x-1}{1}=\frac{y+3}{-3}=\frac{z+1}{1}$ is

3D Geometry

$9$$\sqrt{69}$$69$$\sqrt{99}$

JEE Main 2024 (Online) 31st January Evening ShiftQuestion 73

The shortest distance, between lines $L_1$ and $L_2$, where $L_1:\frac{x-1}{2}=\frac{y+1}{-3}=\frac{z+4}{2}$ and $L_2$ is the line, passing through the points $A(-4,4,3)$, $B(-1,6,3)$ and perpendicular to the line $\frac{x-3}{-2}=\frac{y}{3}=\frac{z-1}{1}$, is

3D Geometry

$\frac{24}{\sqrt{117}}$$\frac{42}{\sqrt{117}}$$\frac{121}{\sqrt{221}}$$\frac{141}{\sqrt{221}}$

JEE Main 2024 (Online) 9th April Morning ShiftQuestion 74

The shortest distance between the lines $\frac{x-3}{4}=\frac{y+7}{-11}=\frac{z-1}{5}$ and $\frac{x-5}{3}=\frac{y-9}{-6}=\frac{z+2}{1}$ is :

3D Geometry

$\frac{178}{\sqrt{563}}$$\frac{179}{\sqrt{563}}$$\frac{185}{\sqrt{563}}$$\frac{187}{\sqrt{563}}$

JEE Main 2025 (Online) 2nd April Evening ShiftQuestion 75

The line $L_1$ is parallel to the vector $\vec{a}=-3\hat{i}+2\hat{j}+4\hat{k}$ and passes through the point $(7,6,2)$ and the line $L_2$ is parallel to the vector $\vec{b}=2\hat{i}+\hat{j}+3\hat{k}$ and passes through the point $(5,3,4)$. The shortest distance between the lines $L_1$ and $L_2$ is :

3D Geometry

$\frac{21}{\sqrt{38}}$$\frac{21}{\sqrt{57}}$$\frac{23}{\sqrt{57}}$$\frac{23}{\sqrt{38}}$