NTA JEE Main 25th June 2022 Shift 2

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

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 same velocity 'u' at two different angles with horizontal attained the same range R. If A and B reached the maximum height $$h_1$$ and $$h_2$$ respectively, then $$R = 4\sqrt{h_1 h_2}$$
Reason R: Product of said heights. $$h_1 h_2 = \frac{u^2\sin^2\theta}{2g} \cdot \frac{u^2\cos^2\theta}{2g}$$

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 :

For a particle in uniform circular motion, the acceleration $$\vec{a}$$ at any point $$P(R, \theta)$$ on the circular path of radius $$R$$ is (when $$\theta$$ is measured from the positive $$x$$-axis and $$v$$ is uniform speed):

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

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

The ratio of specific heats $$\frac{C_p}{C_v}$$ in terms of degree of freedom $$f$$ is given by :

Two metallic plates form a parallel plate capacitor. The distance between the plate is '$$d$$'. A metal sheet of thickness $$\frac{d}{2}$$ and of area equal to area of each plate is introduced between the plates. What will be the ratio of the new capacitance to the original capacitance of the capacitor?

Two cells of the same EMF $$E$$ but different internal resistances, $$r_1$$ and $$r_2$$ are connected in series with an external resistance $$R$$ as shown in the figure. The terminal potential difference across the second cell is found to be zero. The external resistance $$R$$ must then be:

If $$n$$ represents the actual number of deflections in a converted galvanometer of resistance $$G$$ and shunt resistance $$S$$. Then the total current $$I$$ when its figure of merit is $$K$$ will be