JEE Main 2024 Question Paper (31-Jan-2024) (Shift 2)

Question 1

A light string passing over a smooth light fixed pulley connects two blocks of masses $m_{1}$ and $m_{2}$. If the acceleration of the system is $\frac{g}{8}$, then the ratio of masses is

Accepted Answer

$\frac{9}{7}$

Answer

$ \frac{8}{1} $

Answer

$\frac{4}{3}$

Answer

$\frac{5}{3}$

Question 2

A uniform magnetic field of $2 \times 10^{-3} \mathrm{T}$ acts along the positive Y-direction. A rectangular loop of sides $20 \mathrm{cm}$ and $10  \mathrm{cm}$ with a current of $5  \mathrm{A}$ is in the Y-Z plane. The current is in the anticlockwise sense with reference to the negative X-axis. The magnitude and direction of the torque are:

Accepted Answer

$2 	imes 10^{-4} \quad \mathrm{N} \cdot \mathrm{m}$ along negative Z-direction

Answer

$2 	imes 10^{-4} \quad \mathrm{N} \quad \mathrm{m}$ along positive Z &ndash; direction

Answer

$2 	imes 10^{-4} \quad \mathrm{N} \cdot \mathrm{m}$ along positive X-direction

Answer

$2 	imes 10^{-4} \quad \mathrm{N} \cdot \mathrm{m}$ along positive Y-direction

Question 3

The measured value of the length of a simple pendulum is $20  \mathrm{cm}$ with $2 \mathrm{mm}$ accuracy. The time for $50$ oscillations was measured to be $40$ seconds with $1$ second resolution. From these measurements, the accuracy in the measurement of acceleration due to gravity is $N\%$. The value of $N$ is:

Accepted Answer

$6$

Answer

$4$

Answer

$8$

Answer

$5$

Question 4

Force between two point charges $q_{1}$ and $q_{2}$ placed in vacuum at $r$ cm apart is $F$. Force between them when placed in a medium having dielectric constant $K=5$ at $\frac{r}{5}$ cm apart will be:

Accepted Answer

$5F$

Answer

$\frac{F}{25}$

Answer

$\frac{F}{5}$

Answer

$25\,^\circ\mathrm{F}$

Question 5

An AC voltage $ V = 20 \sin 200\pi t $ is applied to a series LCR circuit which drives a current $ I = 10 \sin \left( 200\pi t + \frac{\pi}{3} \right) $. The average power dissipated is:

Accepted Answer

$50 \quad \mathrm{W}$

Answer

$21.6 \quad \mathrm{W}$

Answer

$200 \quad \mathrm{W}$

Answer

$173.2 \quad \mathrm{W}$