NTA JEE Main 27th August 2021 Shift 2 - Physics

Match List-(I) with List-(II).
List-(I)                                                                List-(II)
(a) R$$_H$$ (Rydberg constant)                          (i) kg m$$^{-1}$$ s$$^{-1}$$
(b) $$h$$ (Planck's constant)                            (ii) kg m$$^2$$ s$$^{-1}$$
(c) $$\mu_B$$ (Magnetic field energy density)     (iii) m$$^{-1}$$
(d) $$\eta$$ (coefficient of viscosity)                     (iv) kg m$$^{-1}$$ s$$^{-2}$$
Choose the most appropriate answer from the options given below:

If force (F), length (L) and time (T) are taken as the fundamental quantities. Then what will be the dimension of density:

Water drops are falling from a nozzle of a shower onto the floor from a height of 9.8 m. The drops fall at a regular interval of time. When the first drop strikes the floor, at that instant, the third drop begins to fall. Locate the position of second drop from the floor when the first drop strikes the floor.

A player kicks a football with an initial speed of 25 m s$$^{-1}$$ at an angle of 45° from the ground. What are the maximum height and the time taken by the football to reach at the highest point during motion? (Take g = 10 m s$$^{-2}$$)

The boxes of masses 2 kg and 8 kg are connected by a massless string passing over smooth pulleys. Calculate the time taken by box of mass 8 kg to strike the ground starting from rest. (g = 10 m s$$^{-2}$$)

The height of victoria's falls is 63 m. What is the difference in the temperature of water at the top and at the bottom of the fall? [Given 1 cal = 4.2 J and specific heat of water = 1 cal g$$^{-1}$$ °C$$^{-1}$$]

Two discs have moments of inertia $$I_1$$ and $$I_2$$ about their respective axes perpendicular to the plane and passing through the centre. They are rotating with angular speeds, $$\omega_1$$ and $$\omega_2$$ respectively and are brought into contact face to face with their axes of rotation coaxial. The loss in kinetic energy of the system in the process is given by:

A mass of 50 kg is placed at the center of a uniform spherical shell of mass 100 kg and radius 50 m. If the gravitational potential at a point, 25 m from the center is $$V$$ kg m$$^{-1}$$. The value of $$V$$ is:

If the R.M.S. speed of oxygen molecules at 0°C is 160 m s$$^{-1}$$. Find the R.M.S. speed of hydrogen molecules at 0°C.

Figure shows a rod $$AB$$, which is bent in a 120° circular arc of radius $$R$$. A charge $$(-Q)$$ is uniformly distributed over rod AB. What is the electric field $$\vec{E}$$ at the centre of curvature O?

Three capacitors $$C_1 = 2 \mu$$F, $$C_2 = 6 \mu$$F and $$C_3 = 12 \mu$$F are connected as shown in the figure. Find the ratio of the charges on capacitors $$C_1$$, $$C_2$$ and $$C_3$$ respectively.

For full scale deflection of total 50 divisions, 50 mV voltage is required in galvanometer. The resistance of galvanometer if its current sensitivity is 2 div / mA will be:

The colour coding on a carbon resistor is shown in the given figure. The resistance value of the given resistor is:

A coaxial cable consists of an inner wire of radius $$a$$ surrounded by an outer shell of inner and outer radii $$b$$ and $$c$$ respectively. The inner wire carries an electric current $$i_0$$ which is distributed uniformly across cross-sectional area. The outer shell carries an equal current in opposite direction and distributed uniformly. What will be the ratio of the magnetic field at a distance $$x$$ from the axis when (i) $$x \lt a$$ and (ii) $$a \lt x \lt b$$?

A constant magnetic field of 1 T is applied in the $$x > 0$$ region. A metallic circular ring of radius 1 m is moving with a constant velocity of 1 m s$$^{-1}$$ along the $$x$$-axis. At $$t = 0$$ s, the centre O of the ring is at $$x = -1$$ m. What will be the value of the induced emf in the ring at t = 1 s? (Assume the velocity of the ring does not change.)

Curved surfaces of a plano-convex lens of refractive index $$\mu_1$$ and a plano-concave lens of refractive index $$\mu_2$$ have equal radius of curvature as shown in figure. Find the ratio of radius of curvature to the focal length of the combined lenses.

The light waves from two coherent sources have same intensity $$I_1 = I_2 = I_0$$. In interference pattern the intensity of light at minima is zero. What will be the intensity of light at maxima?

A monochromatic neon lamp with wavelength of 670.5 nm illuminates a photo-sensitive material which has a stopping voltage of 0.48 V. What will be the stopping voltage if the source light is changed with another source of wavelength of 474.6 nm?

For a transistor $$\alpha$$ and $$\beta$$ are given as $$\alpha = \frac{I_c}{I_E}$$ and $$\beta = \frac{I_c}{I_B}$$. Then the correct relation between $$\alpha$$ and $$\beta$$ will be:

An antenna is mounted on a 400 m tall building. What will be the wavelength of signal that can be radiated effectively by the transmission tower upto a range of 44 km?

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 _________ $$\Omega$$.