JEE Main 2023 Question Paper (15-Apr-2023) (Shift 1)

Question 1

A flask contains Hydrogen and Argon in the ratio $2:1$ by mass. The temperature of the mixture is $30^\circ \mathrm{C}$. The ratio of average kinetic energy per molecule of the two gases $\left(\frac{K_{\mathrm{argon}}}{K_{\mathrm{hydrogen}}}\right)$ is: (Given: Atomic Weight of $Ar = 39.9$)

Accepted Answer

$1$

Answer

$2$

Answer

$39.9$

Answer

$\frac{39.9}{2}$

Question 2

A $12 \ \mathrm{V}$ battery connected to a coil of resistance $6 \ \Omega$ through a switch drives a constant current in the circuit. The switch is opened in $1 \ \mathrm{ms}$. The emf induced across the coil is $20 \ \mathrm{V}$. The inductance of the coil is :

Accepted Answer

$10 \quad \mathrm{mH}$

Answer

$8 \quad \mathrm{mH}$

Answer

$5\quad \mathrm{mH}$

Answer

$12 \quad \mathrm{mH}$

Question 3

Two identical particles each of mass $m$ go round a circle of radius $a$ under the action of their mutual gravitational attraction. The angular speed of each particle will be:

Accepted Answer

$\sqrt{\frac{G m}{4 a^{3}}}$

Answer

$ \sqrt{\frac{G m}{a^{3}}} $

Answer

$\sqrt{\frac{G m}{8 a^{3}}}$

Answer

$\sqrt{\frac{G m}{2 a^{3}}}$

Question 4

The position vector of a particle related to time $t$ is given by $\overrightarrow{r} = \left(10t \hat{i} + 15 t^{2} \hat{j} + 7 \hat{k}\right) \mathrm{m}$. The direction of net force experienced by the particle is :

Accepted Answer

Positive $y$-axis

Answer

Positive $x$-axis

Answer

$\mathrm{In} \quad x - y 	ext{ plane}$

Answer

Positive $z$-axis

Question 5

The half-life of a radioactive nucleus is $5$ years. The fraction of the original sample that would decay in $15$ years is:

Accepted Answer

$\frac{7}{8}$

Answer

$\frac{1}{8}$

Answer

$\frac{1}{4}$

Answer

$\frac{3}{4}$