JEE Main 2023 Question Paper (11-Apr-2023) (Shift 1)

Question 1

The radii of two planets $ A $ and $ B $ are $ R $ and $ 4R $ and their densities are $ \rho $ and $ \frac{\rho}{3} $ respectively. The ratio of acceleration due to gravity at their surfaces $ \left(g_{A} : g_{B}\right) $ will be

Accepted Answer

$3:4$

Answer

$4:3$

Answer

$1:16$

Answer

$3:16$

Question 2

The free space inside a current carrying toroid is filled with a material of susceptibility $ 2 \times 10^{-2} $. The percentage increase in the value of magnetic field inside the toroid will be

Accepted Answer

$2\%$

Answer

$0.2\%$

Answer

$0.1\%$

Answer

$1\%$

Question 3

Three vessels of equal volume contain gases at the same temperature and pressure. The first vessel contains neon (monoatomic), the second contains chlorine (diatomic), and the third contains uranium hexafluoride (polyatomic). Arrange these on the basis of their root mean square speed $ \left(v_{\text{rms}}\right) $ and choose the correct answer from the options given below:

Accepted Answer

${\mathrm{v}}_{rms}(\mathrm{mono}) > {\mathrm{v}}_{rms}(\mathrm{dia}) > {\mathrm{v}}_{rms}(\mathrm{poly})$

Answer

${V}_{rms}(\mathrm{mono}) = {V}_{rms}(\mathrm{dia}) = {V}_{rms}(\mathrm{poly})$

Answer

${\mathrm{v}}_{rms}(\mathrm{mono}) < {\mathrm{v}}_{rms}(\mathrm{dia}) < {\mathrm{v}}_{rms}(\mathrm{poly})$

Answer

${\mathrm{v}}_{\mathrm{rms}}(\mathrm{dia}) < {\mathrm{v}}_{\mathrm{rms}}(\mathrm{poly}) < {\mathrm{v}}_{\mathrm{rms}}(\mathrm{mono})$

Question 4

Two radioactive elements $A$ and $B$ initially have the same number of atoms. The half-life of $A$ is the same as the average life of $B$. If $\lambda_{A}$ and $\lambda_{B}$ are the decay constants of $A$ and $B$ respectively, then choose the correct relation from the given options.

Accepted Answer

$ \lambda_{A} = \lambda_{B} \ln 2 $

Answer

$ \lambda_{A} \ln 2 = \lambda_{B} $

Answer

$\lambda_{A} = \lambda_{B}$

Answer

$ \lambda_{A} = 2 \lambda_{B} $

Question 5

The electric field in an electromagnetic wave is given as
\[ \overrightarrow{E} = 20 \sin \omega \left(t - \frac{x}{c}\right) \overrightarrow{j} \quad \mathrm{N\,C}^{-1}, \] where $ \omega $ and $ c $ are the angular frequency and velocity of the electromagnetic wave, respectively. The energy contained in a volume of $ 5 \times 10^{-4} \ \mathrm{m}^3 $ will be
(Given $ \epsilon_0 = 8.85 \times 10^{-12} \ \mathrm{C}^2 \, \mathrm{N}^{-1} \, \mathrm{m}^{-2} $)

Accepted Answer

$8.85 	imes 10^{-13} \quad \mathrm{J}$

Answer

$88.5 	imes 10^{-13} \quad \mathrm{J}$

Answer

$17.7 	imes 10^{-13} \quad \mathrm{J}$

Answer

$28.5 	imes 10^{-13} \quad \mathrm{J}$