JEE Main 2022 Question Paper (25-Jul-2022) (Shift 2)

Question 1

In $\mathrm{AM}$ modulation, a signal is modulated on a carrier wave such that maximum and minimum amplitude are found to be $6 \quad \mathrm{V}$ and $2 \quad \mathrm{V}$ respectively. The modulation index is

Accepted Answer

$50\%$

Answer

$100\%$

Answer

$80\%$

Answer

$60\%$

Question 2

The electric current in a circular coil of $2$ turns produces a magnetic induction $B_{1}$ at its centre. The coil is unwound and is rewound into a circular coil of $5$ turns and the same current produces a magnetic induction $B_{2}$ at its centre.
The ratio of $\frac{B_{2}}{B_{1}}$ is:

Accepted Answer

$\frac{25}{4}$

Answer

$\frac{5}{2}$

Answer

$\frac{5}{4}$

Answer

$\frac{25}{2}$

Question 3

A drop of liquid of density $ho$ is floating half immersed in a liquid of density $\sigma$ and surface tension $7.5 	imes 10^{-4}  \mathrm{N}  \mathrm{cm}^{-1}$. The radius of the drop in $\mathrm{cm}$ will be: (Take: $g = 10  \mathrm{m}  \mathrm{s}^{-2}$)

Accepted Answer

$\frac{15}{\sqrt{2\rho - \sigma}}$

Answer

$\frac{15}{\sqrt{\rho - \sigma}}$

Answer

$\frac{3}{2\sqrt{\rho - \sigma}}$

Answer

$\frac{3}{20\sqrt{2\rho - \sigma}}$

Question 4

Two billiard balls of mass $0.05  \mathrm{kg}$ each moving in opposite directions with $10  \mathrm{m} \mathrm{s}^{-1}$ collide and rebound with the same speed. If the time duration of contact is $t = 0.005  \mathrm{s}$, then what is the force exerted on the ball due to each other?

Accepted Answer

$200  \mathrm{N}$

Answer

$100  \mathrm{N}$

Answer

$300  \mathrm{N}$

Answer

$400  \mathrm{N}$

Question 5

For a free body diagram shown in the figure, the four forces are applied in the '$x$' and '$y$' directions. What additional force must be applied and at what angle with the positive $x$-axis so that the net acceleration of the body is zero?

Accepted Answer

$ \sqrt{2} \quad \mathrm{N}, 45^\circ $

Answer

$ \sqrt{2} \quad \mathrm{N}, 135^\circ $

Answer

$ \frac{2}{\sqrt{3}} \quad \mathrm{N}, 30^\circ $

Answer

$2 \quad \mathrm{N}, 45^\circ$