1
JEE Main 2025 (Online) 22nd January Evening Shift
MCQ (Single Correct Answer)
+4
-1

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : A simple pendulum is taken to a planet of mass and radius, 4 times and 2 times, respectively, than the Earth. The time period of the pendulum remains same on earth and the planet.

Reason (R): The mass of the pendulum remains unchanged at Earth and the other planet.

In the light of the above statements, choose the correct answer from the options given below :

A
Both (A) and (R) are true and (R) is the correct explanation of (A)
B
(A) is false but (R) is true
C
(A) is true but (R) is false
D
Both (A) and (R) are true but (R) is NOT the correct explanation of (A)
2
JEE Main 2025 (Online) 22nd January Evening Shift
MCQ (Single Correct Answer)
+4
-1

Given are statements for certain thermodynamic variables,

(A) Internal energy, volume $(\mathrm{V})$ and mass $(\mathrm{M})$ are extensive variables.

(B) Pressure (P), temperature ( T ) and density ( $\rho$ ) are intensive variables.

(C) Volume (V), temperature (T) and density ( $\rho$ ) are intensive variables.

(D) Mass (M), temperature (T) and internal energy are extensive variables.

Choose the correct answer from the options given below :

A
(C) and (D) Only
B
(A) and (B) Only
C
(D) and (A) Only
D
(B) and (C) Only
3
JEE Main 2025 (Online) 22nd January Evening Shift
MCQ (Single Correct Answer)
+4
-1

The torque due to the force $(2 \hat{i}+\hat{j}+2 \hat{k})$ about the origin, acting on a particle whose position vector is $(\hat{i}+\hat{j}+\hat{k})$, would be

A
$\hat{j}+\hat{k}$
B
$\hat{i}-\hat{k}$
C
$\hat{i}-\hat{j}+\hat{k}$
D
$\hat{i}+\hat{k}$
4
JEE Main 2025 (Online) 22nd January Evening Shift
MCQ (Single Correct Answer)
+4
-1

Which one of the following is the correct dimensional formula for the capacitance in F ? $\mathrm{M}, \mathrm{L}, \mathrm{T}$ and $C$ stand for unit of mass, length, time and charge,

A
$[\mathrm{F}]=\left[\mathrm{CM}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^2\right]$
B
$[\mathrm{F}]=\left[\mathrm{C}^2 \mathrm{M}^{-2} \mathrm{~L}^2 \mathrm{~T}^2\right]$
C
$[\mathrm{F}]=\left[\mathrm{C}^2 \mathrm{M}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^2\right]$
D
$[\mathrm{F}]=\left[\mathrm{CM}^{-2} \mathrm{~L}^{-2} \mathrm{~T}^{-2}\right]$
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