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

Question 1

Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R. Assertion A: Two identical balls $A$ and $B$ thrown with the same velocity $u$ at two different angles with the horizontal attain the same range $R$. If $A$ and $B$ reach the maximum heights $h_1$ and $h_2$ respectively, then $ R = 4 \sqrt{h_1 h_2}. $ Reason R: The product of the said heights is $ h_1 h_2 = \left(\frac{u^2 \sin^2 	heta}{2g}ight) \cdot \left(\frac{u^2 \cos^2 	heta}{2g}ight). $

Accepted Answer

Both $ A $ and $ R $ are true and $ R $ is the correct explanation of $ A $.

Answer

Both A and R are true but R is NOT the correct explanation of A.

Answer

A is true but R is false.

Answer

A is false but R is true.

Question 2

Two buses $P$ and $Q$ start from a point at the same time and move in a straight line. Their positions are represented by $ x_{P}(t) = \alpha t + \beta t^{2} 	ext{and} x_{Q}(t) = ft - t^{2}. $ At what time do both the buses have the same velocity?

Accepted Answer

$\frac{f - \alpha}{2 \left(1 + \beta \right)}$

Answer

$\frac{\alpha - f}{1 + \beta}$

Answer

$\frac{\alpha + f}{2(\beta - 1)}$

Answer

$\frac{\alpha + f}{2\left(1 + \beta\right)}$

Question 3

A disc with a flat small bottom beaker placed on it at a distance $R$ from its center is revolving about an axis passing through the center and perpendicular to its plane with an angular velocity $\omega$. The coefficient of static friction between the bottom of the beaker and the surface of the disc is $\mu$. The beaker will revolve with the disc if :

Accepted Answer

$ R \leq \frac{\mu g}{\omega^{2}} $

Answer

$ R \leq \frac{\mu g}{2 \omega^{2}} $

Answer

$ R \geq \frac{\mu g}{2 \omega^{2}} $

Answer

$ R \geq \frac{\mu g}{\omega^{2}} $

Question 4

A solid metallic cube having total surface area $24 \mathrm{m}^2$ is uniformly heated. If its temperature is increased by $10^\circ \mathrm{C}$, calculate the increase in volume of the cube. (Given $\alpha = 5.0 	imes 10^{-4} \, {}^\circ \mathrm{C}^{-1}$).

Accepted Answer

$1.2 	imes 10^{5} \, \mathrm{cm}^{3}$

Answer

$2.4 	imes 10^{6} \, \mathrm{cm}^{3}$

Answer

$6 	imes 10^{4} \, \mathrm{cm}^{3}$

Answer

$4.8 	imes 10^{5} \quad \mathrm{cm}^{3}$

Question 5

A copper block of mass $5.0\mathrm{kg}$ is heated to a temperature of $500^\circ \mathrm{C}$ and is placed on a large ice block. What is the maximum amount of ice that can melt?
[Specific heat of copper: $0.39\, \mathrm{J\,g}^{-1}{}^\circ \mathrm{C}^{-1}$ and latent heat of fusion of water: $335\mathrm{J\,g}^{-1}$]

Accepted Answer

$2.9 \quad \mathrm{kg}$

Answer

$1.5 \quad \mathrm{kg}$

Answer

$5.8 \quad \mathrm{kg}$

Answer

$3.8 \quad \mathrm{kg}$