JEE Maths PYQ Practice, chapter-wise

JEE Main 2021 (Online) 27th August Evening ShiftQuestion 21

The angle between the straight lines, whose direction cosines are given by the equations $2l+2m-n=0$ and $mn+nl+lm=0$, is :

3D Geometry

$\frac{\pi}{3}$$\cos^{-1}\left(\frac{8}{9}\right)$$\frac{\pi}{2}$$\pi-\cos^{-1}\left(\frac{4}{9}\right)$

JEE Main 2021 (Online) 3rd August Evening ShiftQuestion 22

Let $L_1$ and $L_2$ be two lines passing through the points $P(b-c,c-a,a-b)$ and $Q\left(\frac{1}{l},\frac{1}{m},\frac{1}{n}\right)$ respectively, where $\frac{1}{l},\frac{1}{m}$ and $\frac{1}{n}$ are the $a^{\text{th}}$, $b^{\text{th}}$ and $c^{\text{th}}$ terms of an Arithmetic Progression. If $L_1$ and $L_2$ intersect at the origin, then an angle between them is

3D Geometry

$\frac{\pi}{3}$$\frac{\pi}{2}$$\frac{\pi}{4}$$\frac{\pi}{6}$

JEE Main 2021 (Online) 25th July Morning ShiftQuestion 23

Let the foot of perpendicular from a point $P(1,2,-1)$ to the straight line $L:\frac{x}{1}=\frac{y}{0}=\frac{z}{-1}$ be $N$. Let a line be drawn from $P$ parallel to the plane $x+y+2z=0$ which meets $L$ at point $Q$. If $\alpha$ is the acute angle between the lines $PN$ and $PQ$, then $\cos\alpha$ is equal to :

3D Geometry

$\frac{\sqrt{3}}{2}$$\frac{1}{\sqrt{3}}$$\frac{1}{\sqrt{5}}$$\frac{1}{2\sqrt{3}}$

JEE Main 2021 (Online) 27th August Evening ShiftQuestion 24

The equation of the plane passing through the line of intersection of the planes $\vec{r}\cdot\left(\hat{i}+\hat{j}+\hat{k}\right)=1$ and $\vec{r}\cdot\left(2\hat{i}+3\hat{j}-\hat{k}\right)+4=0$ and parallel to the $x$-axis is :

3D Geometry

$\vec{r}\cdot\left(\hat{i}-3\hat{k}\right)+6=0$$\vec{r}\cdot\left(\hat{i}+3\hat{k}\right)+6=0$$\vec{r}\cdot\left(\hat{j}-3\hat{k}\right)-6=0$$\vec{r}\cdot\left(\hat{j}-3\hat{k}\right)+6=0$

JEE Main 2021 (Online) 27th August Morning ShiftQuestion 25

The distance of the point $(1,-2,3)$ from the plane $x-y+z=5$ measured parallel to a line, whose direction ratios are $2,3,-6$ is :

3D Geometry

$2$$3$$1$$5$