JEE Maths PYQ Practice, chapter-wise

JEE Main 2022 (Online) 26th June Evening ShiftQuestion 116

If the lines $\vec{r}=\left(\hat{i}-\hat{j}+\hat{k}\right)+\lambda\left(3\hat{j}-\hat{k}\right)$ and $\vec{r}=\left(\alpha\hat{i}-\hat{j}\right)+\mu\left(2\hat{i}-3\hat{k}\right)$ are co-planar, then the distance of the plane containing these two lines from the point $(\alpha,0,0)$ is :

3D Geometry

$\frac{2}{9}$$\frac{2}{11}$$\frac{4}{11}$$2$

JEE Main 2022 (Online) 28th June Morning ShiftQuestion 117

Let the plane $P:\vec{r}\cdot\vec{a}=d$ contain the line of intersection of two planes $\vec{r}\cdot\left(\hat{i}+3\hat{j}-\hat{k}\right)=6$ and $\vec{r}\cdot\left(-6\hat{i}+5\hat{j}-\hat{k}\right)=7$. If the plane $P$ passes through the point $\left(2,3,\frac{1}{2}\right)$, then the value of $\frac{|13\vec{a}|^{2}}{d^{2}}$ is equal to

3D Geometry

$90$$93$$95$$97$

JEE Main 2022 (Online) 25th July Evening ShiftQuestion 118

The shortest distance between the lines $\frac{x+7}{-6}=\frac{y-6}{7}=z$ and $\frac{7-x}{2}=y-2=z-6$ is

3D Geometry

$2\sqrt{29}$$1$$\sqrt{\frac{37}{29}}$$\frac{\sqrt{29}}{2}$

JEE Main 2022 (Online) 28th July Evening ShiftQuestion 119

A plane $P$ is parallel to two lines whose direction ratios are $-2,1,-3$ and $-1,2,-2$ and it contains the point $(2,2,-2)$. Let $P$ intersect the co-ordinate axes at the points $A,B,C$ making the intercepts $\alpha,\beta,\gamma$. If $V$ is the volume of the tetrahedron $OABC$, where $O$ is the origin, and $p=\alpha+\beta+\gamma$, then the ordered pair $(V,p)$ is equal to :

3D Geometry

$(48,-13)$$(24,-13)$$(48,11)$$(24,-5)$

JEE Main 2022 (Online) 29th June Evening ShiftQuestion 120

Let $Q$ be the mirror image of the point $P(1,2,1)$ with respect to the plane $x+2y+2z=16$. Let $T$ be a plane passing through the point $Q$ and contains the line $\vec{r}=-\hat{k}+\lambda\left(\hat{i}+\hat{j}+2\hat{k}\right)$, $\lambda\in\mathbf{R}$. Then, which of the following points lies on $T$?

3D Geometry

$(2,1,0)$$(1,2,1)$$(1,2,2)$$(1,3,2)$