JEE Main 2023 Question Paper (13-Apr-2023) (Shift 1)

Question 1

A disc is rolling without slipping on a surface. The radius of the disc is $ R $. At $ t = 0 $, the topmost point on the disc is $ A $ as shown in the figure. When the disc completes half of its rotation, the displacement of point $ A $ from its initial position is

Accepted Answer

$R \sqrt{\pi^{2} + 4}$

Answer

$2R$

Answer

$ \mathrm{R} \sqrt{\pi^{2} + 1} $

Answer

$2R\sqrt{1 + 4\pi^{2}}$

Question 2

Different combinations of $3$ resistors of equal resistance $R$ are shown in the figures. The increasing order for power dissipation is:(A) (B) (C) (D)

Accepted Answer

${P}_{C} < {P}_{B} < {P}_{A} < {P}_{D}$

Answer

${P}_{B} < {P}_{C} < {P}_{D} < {P}_{A}$

Answer

${P}_{C} < {P}_{D} < {P}_{A} < {P}_{B}$

Answer

${P}_{A} < {P}_{B} < {P}_{C} < {P}_{D}$

Question 3

A planet having mass $9 \quad {\mathrm{M}}_{\mathrm{e}}$ and radius $4 {\mathrm{R}}_{\mathrm{e}},$ where ${\mathrm{M}}_{\mathrm{e}}$ and ${\mathrm{R}}_{\mathrm{e}}$ are the mass and radius of Earth respectively, has escape velocity in $\mathrm{km} \quad \mathrm{s}^{-1}$ given by: (Given escape velocity on Earth $V_{\mathrm{e}} = 11.2 	imes 10^{3} \quad \mathrm{m} \quad \mathrm{s}^{-1}$)

Accepted Answer

$16.8$

Answer

$67.2$

Answer

$11.2$

Answer

$33.6$

Question 4

${}_{92}^{238}\mathrm{A} 	o {}_{90}^{234}\mathrm{B} + {}_{2}^{4}\mathrm{D} + \mathrm{Q}$ In the given nuclear reaction, the approximate amount of energy released will be: [Given, mass of ${}_{92}^{238}\mathrm{A} = 238.05079 	imes 931.5 \quad \mathrm{MeV} \quad \mathrm{c}^{-2}$, mass of ${}_{90}^{234}\mathrm{B} = 234.04363 	imes 931.5 \quad \mathrm{MeV} \quad \mathrm{c}^{-2}$, mass of ${}_{2}^{4}\mathrm{D} = 4.00260 	imes 931.5 \quad \mathrm{MeV} \quad \mathrm{c}^{-2}$]

Accepted Answer

$4.25\,\mathrm{MeV}$

Answer

$3.82\,\mathrm{MeV}$

Answer

$5.9\,\mathrm{MeV}$

Answer

$2.12\,\mathrm{MeV}$

Question 5

The difference between threshold wavelengths for two metal surfaces $A$ and $B$ having work functions ${\varphi}_{A} = 9\,\mathrm{eV}$ and ${\varphi}_{B} = 4.5\,\mathrm{eV}$ in $\mathrm{nm}$ is:Given, $hc = 1242 \mathrm{eV} \cdot \mathrm{nm}$

Accepted Answer

$138$

Answer

$540$

Answer

$276$

Answer

$264$