1
JEE Main 2025 (Online) 2nd April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
The line $\mathrm{L}_1$ is parallel to the vector $\overrightarrow{\mathrm{a}}=-3 \hat{i}+2 \hat{j}+4 \hat{k}$ and passes through the point $(7,6,2)$ and the line $\mathrm{L}_2$ is parallel to the vector $\overrightarrow{\mathrm{b}}=2 \hat{i}+\hat{j}+3 \hat{k}$ and passes through the point $(5,3,4)$. The shortest distance between the lines $L_1$ and $L_2$ is :
A
$\frac{23}{\sqrt{38}}$
B
$\frac{21}{\sqrt{38}}$
C
$\frac{23}{\sqrt{57}}$
D
$\frac{21}{\sqrt{57}}$
2
JEE Main 2025 (Online) 2nd April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let the vertices Q and R of the triangle PQR lie on the line $\frac{x+3}{5}=\frac{y-1}{2}=\frac{z+4}{3}, \mathrm{QR}=5$ and the coordinates of the point $P$ be $(0,2,3)$. If the area of the triangle $P Q R$ is $\frac{m}{n}$ then :

A
$2 \mathrm{~m}-5 \sqrt{21} \mathrm{n}=0$
B
$\mathrm{m}-5 \sqrt{21} \mathrm{n}=0$
C
$5 \mathrm{~m}-21 \sqrt{2} \mathrm{n}=0$
D
$5 \mathrm{~m}-2 \sqrt{21} \mathrm{n}=0$
3
JEE Main 2025 (Online) 2nd April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $A B C D$ be a tetrahedron such that the edges $A B, A C$ and $A D$ are mutually perpendicular. Let the areas of the triangles $\mathrm{ABC}, \mathrm{ACD}$ and ADB be 5,6 and 7 square units respectively. Then the area (in square units) of the $\triangle B C D$ is equal to :

A
$\sqrt{110}$
B
12
C
$\sqrt{340}$
D
$7 \sqrt{3}$
4
JEE Main 2025 (Online) 29th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let a straight line $L$ pass through the point $P(2, -1, 3)$ and be perpendicular to the lines $ \frac{x - 1}{2} = \frac{y + 1}{1} = \frac{z - 3}{-2} $ and $ \frac{x - 3}{1} = \frac{y - 2}{3} = \frac{z + 2}{4} $. If the line $L$ intersects the $yz$-plane at the point $Q$, then the distance between the points $P$ and $Q$ is:

A

$\sqrt{10}$

B

$2$

C

$2\sqrt{3}$

D

$3$

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