1
JEE Main 2025 (Online) 22nd January Morning Shift
Numerical
+4
-1
Change Language

Let $\mathrm{L}_1: \frac{x-1}{3}=\frac{y-1}{-1}=\frac{z+1}{0}$ and $\mathrm{L}_2: \frac{x-2}{2}=\frac{y}{0}=\frac{z+4}{\alpha}, \alpha \in \mathbf{R}$, be two lines, which intersect at the point $B$. If $P$ is the foot of perpendicular from the point $A(1,1,-1)$ on $L_2$, then the value of $26 \alpha(\mathrm{~PB})^2$ is _________ .

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2
JEE Main 2025 (Online) 22nd January Morning Shift
Numerical
+4
-1
Change Language

Let $A$ be a square matrix of order 3 such that $\operatorname{det}(A)=-2$ and $\operatorname{det}(3 \operatorname{adj}(-6 \operatorname{adj}(3 A)))=2^{m+n} \cdot 3^{m n}, m>n$. Then $4 m+2 n$ is equal to __________.

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3
JEE Main 2025 (Online) 22nd January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

A small point of mass $m$ is placed at a distance $2 R$ from the centre ' $O$ ' of a big uniform solid sphere of mass M and radius R . The gravitational force on ' m ' due to M is $\mathrm{F}_1$. A spherical part of radius $\mathrm{R} / 3$ is removed from the big sphere as shown in the figure and the gravitational force on m due to remaining part of $M$ is found to be $F_2$. The value of ratio $F_1: F_2$ is

JEE Main 2025 (Online) 22nd January Morning Shift Physics - Gravitation Question 10 English

A
11 : 10
B
12 : 11
C
16 : 9
D
12 : 9
4
JEE Main 2025 (Online) 22nd January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If $B$ is magnetic field and $\mu_0$ is permeability of free space, then the dimensions of $\left(B / \mu_0\right)$ is

A
$\mathrm{MT}^{-2} \mathrm{~A}^{-1}$
B
$\mathrm{L}^{-1} \mathrm{~A}$
C
$\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~A}^{-1}$
D
$\mathrm{LT}^{-2} \mathrm{~A}^{-1}$
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