NTA JEE Main 27th August 2021 Shift 2

A bullet of 10 g, moving with velocity $$v$$, collides head-on with the stationary bob of a pendulum and recoils with velocity 100 m s$$^{-1}$$. The length of the pendulum is 0.5 m and mass of the bob is 1 kg. The minimum value of $$v$$ in m s$$^{-1}$$, so that the pendulum describes a circle. (Assume the string to be inextensible and g = 10 m s$$^{-2}$$)

Wires $$W_1$$ and $$W_2$$ are made of same material having the breaking stress of $$1.25 \times 10^9$$ N m$$^{-2}$$. $$W_1$$ and $$W_2$$ have cross-sectional area of $$8 \times 10^{-7}$$ m$$^2$$ and $$4 \times 10^{-7}$$ m$$^2$$, respectively. Masses of 20 kg and 10 kg hang from them as shown in the figure. The maximum mass that can be placed in the pan without breaking the wires is _________ kg (Use g = 10 m s$$^{-2}$$)

A heat engine operates between a cold reservoir at temperature $$T_2 = 400$$ K and a hot reservoir at temperature $$T_1$$. It takes 300 J of heat from the hot reservoir and delivers 240 J of heat to the cold reservoir in a cycle. The minimum temperature of the hot reservoir has to be _________.

Two simple harmonic motion, are represented by the equations
$$y_1 = 10\sin\left(3\pi t + \frac{\pi}{3}\right)$$; $$y_2 = 5\left(\sin 3\pi t + \sqrt{3}\cos 3\pi t\right)$$
Ratio of amplitude of $$y_1$$ to $$y_2$$ = $$x$$ : 1. The value of $$x$$ is _________.

A tuning fork is vibrating at 250 Hz. The length of the shortest closed organ pipe that will resonate with the tuning fork will be _________ cm. (Take speed of sound in air as 340 m s$$^{-1}$$)

The ratio of the equivalent resistance of the network (shown in figure) between the points $$a$$ and $$b$$ when switch is open and switch is closed is $$x : 8$$. The value of $$x$$ is _________.

An AC circuit has an inductor and a resistor of resistance $$R$$ in series, such that $$X_L = 3R$$. Now, a capacitor is added in series such that $$X_C = 2R$$. The ratio of the new power factor with the old power factor of the circuit is $$\sqrt{5} : x$$. The value of $$x$$ is _________.

A plane electromagnetic wave with a frequency of 30 MHz travels in free space. At a particular point in space and time, the electric field is 6 V m$$^{-1}$$. The magnetic field at this point will be $$x \times 10^{-8}$$ T. The value of $$x$$ is _________.

$$X$$ different wavelength may be observed in the spectrum from a hydrogen sample if the atoms are excited to states with principal quantum number $$n = 6$$? The value of $$X$$ is _________.

A zener diode of power rating 2 W is to be used as a voltage regulator. If the zener diode has a breakdown of 10 V and it has to regulate voltage fluctuated between 6 V and 14 V, the value of $$R_s$$ for safe operation should be _________ $$\Omega$$.