JEE Main 2024 Question Paper (27-Jan-2024) (Shift 1)

Question 1

Position of an ant ($\mathrm{S}$ in metres) moving in the $\mathrm{Y}-\mathrm{Z}$ plane is given by $ \mathrm{S} = 2 t^{2} \hat{\mathrm{j}} + 5 \hat{\mathrm{k}} $ (where $t$ is in seconds). The magnitude and direction of the velocity of the ant at $t = 1 \quad \mathrm{s}$ will be:

Accepted Answer

$4 \quad \mathrm{m} \quad \mathrm{s}^{-1}$ in $y$-direction

Answer

$16\quad \mathrm{m} \quad \mathrm{s}^{-1}$ in y-direction

Answer

$4 \quad \mathrm{m} \quad \mathrm{s}^{-1}$ in $x$-direction

Answer

$9 \quad \mathrm{m} \quad \mathrm{s}^{-1}$ in z-direction

Question 2

Given below are two statements : Statement (I) : Viscosity of gases is greater than that of liquids. Statement (II) : Surface tension of a liquid decreases due to the presence of insoluble impurities. In the light of the above statements, choose the most appropriate answer from the options given below :

Accepted Answer

Statement I is incorrect but Statement II is correct.

Answer

Statement I is correct but statement II is incorrect.

Answer

Both Statement I and Statement II are incorrect.

Answer

Both Statement I and Statement II are correct

Question 3

If the refractive index of the material of a prism is $ \cot\left(\frac{A}{2}\right) $, where $ A $ is the angle of the prism, then the angle of minimum deviation will be

Accepted Answer

$ \pi - 2 \quad \mathrm{A} $

Answer

$ \frac{\pi}{2} - 2 \quad \mathrm{A} $

Answer

$ \pi - \mathrm{A} $

Answer

$\frac{\pi}{2} - A$

Question 4

A proton moving with a constant velocity passes through a region of space without any change in its velocity. If $\overrightarrow{E}$ and $\overrightarrow{B}$ represent the electric and magnetic fields respectively, then the region of space may have : (A) $E = 0, \quad B = 0$ (B) $E = 0, \quad B 
e 0$ (C) $E 
e 0, \quad B = 0$ (D) $E 
e 0, \quad B 
e 0$ Choose the most appropriate answer from the options given below :

Accepted Answer

(A), (B) and (D) only

Answer

(A), (B) and (C) only

Answer

(A), (C) and (D) only

Answer

(B), (C) and (D) only

Question 5

The acceleration due to gravity on the surface of Earth is $ g $. If the diameter of Earth reduces to half of its original value and the mass remains constant, then the acceleration due to gravity on the surface of Earth would be:

Accepted Answer

$4g$

Answer

$ \frac{g}{4} $

Answer

$2g$

Answer

$ \frac{g}{2} $