NTA JEE Main 27th July 2021 Shift 2 - Physics

A physical quantity $$y$$ is represented by the formula $$y = m^2 r^{-4} g^x l^{-\frac{3}{2}}$$. If the percentage errors found in $$y$$, $$m$$, $$r$$, $$l$$ and $$g$$ are 18, 1, 0.5, 4 and $$p$$ respectively, then find the value of $$x$$ and $$p$$.

Match List I with List II.
    List-I                                                             List-II
a. Capacitance, C                                  i.   $$M^1 L^1 T^{-3} A^{-1}$$
b. Permittivity of free space, $$\varepsilon_0$$          ii.  $$M^{-1} L^{-3} T^4 A^2$$
c. Permeability of free space, $$\mu_0$$       iii. $$M^{-1} L^{-2} T^4 A^2$$
d. Electric field, E                                  iv. $$M^1 L^1 T^{-2} A^{-2}$$
Choose the correct answer from the options given below:

A particle of mass $$M$$ originally at rest is subjected to a force whose direction is constant but magnitude varies with time according to the relation $$F = F_0\left[1 - \left(\frac{t-T}{T}\right)^2\right]$$ where $$F_0$$ and $$T$$ are constants. The force acts only for the time interval $$2T$$. The velocity $$v$$ of the particle after time $$2T$$ is:

Given below is the plot of a potential energy function U(x) for a system, in which a particle is in one dimensional motion, while a conservative force F(x) acts on it. Suppose that $$E_{mech} = 8$$ J, the incorrect statement for this system is:

An automobile of mass $$m$$ accelerates starting from the origin and initially at rest, while the engine supplies constant power $$P$$. The position is given as a function of time by:

Two identical particles of mass 1 kg each go round a circle of radius $$R$$, under the action of their mutual gravitational attraction. The angular speed of each particle is:

The planet Mars has two moons, if one of them has a period 7 hours, 30 minutes and an orbital radius of $$9.0 \times 10^3$$ km. Find the mass of Mars.
$$\left\{\text{Given } \frac{4\pi^2}{G} = 6 \times 10^{11} \text{ N}^{-1} \text{ m}^{-2} \text{ kg}^2\right\}$$

A raindrop with radius R = 0.2 mm falls from a cloud at a height h = 2000 m above the ground. Assume that the drop is spherical throughout its fall and the force of buoyancy may be neglected, then the terminal speed attained by the raindrop is: [Density of water $$f_w = 1000$$ kg m$$^{-3}$$ and Density of air $$f_a = 1.2$$ kg m$$^{-3}$$, g = 10 m/s$$^2$$, Coefficient of viscosity of air = $$1.8 \times 10^{-5}$$ N s m$$^{-2}$$]

One mole of an ideal gas is taken through an adiabatic process where the temperature rises from 27°C to 37°C. If the ideal gas is composed of polyatomic molecule that has 4 vibrational modes, which of the following is true? [R = 8.314 J mol$$^{-1}$$ K$$^{-1}$$]

Two Carnot engines $$A$$ and $$B$$ operate in series such that engine A absorbs heat at $$T_1$$ and rejects heat to a sink at temperature T. Engine B absorbs half of the heat rejected by Engine $$A$$ and rejects heat to the sink at $$T_3$$. When workdone in both the cases is equal, to value of T is:

An object of mass 0.5 kg is executing simple harmonic motion. It amplitude is 5 cm and time period (T) is 0.2 s. What will be the potential energy of the object at an instant $$t = \frac{T}{4}$$ s starting from mean position. Assume that the initial phase of the oscillation is zero.

A simple pendulum of mass $$'m'$$, length $$'l'$$ and charge $$'+q'$$ suspended in the electric field produced by two conducting parallel plates as shown. The value of deflection of pendulum in equilibrium position will be

What will be the magnitude of the electric field at point $$O$$ as shown in the figure? Each side of the figure is $$l$$ and perpendicular to the other.

The resistance of a conductor at 15°C is 16 $$\Omega$$ and at 100°C is 20 $$\Omega$$. What will be the temperature coefficient of resistance of the conductor?

Figure A and B shown two long straight wires of circular cross-section ($$a$$ and $$b$$ with $$a < b$$), carrying current $$I$$ which is uniformly distributed across the cross-section. The magnitude of magnetic field $$B$$ varies with radius $$r$$ and can be represented as:

A 100$$\Omega$$ resistance, a 0.1$$\mu$$F capacitor and an inductor are connected in series across a 250 V supply at variable frequency. Calculate the value of inductance of inductor at which resonance will occur. Given that the resonant frequency is 60 Hz.

The expected graphical representation of the variation of angle of deviation '$$\delta$$' with angle of incidence 'i' in a prism is:

An electron and proton are separated by a large distance. The electron starts approaching the proton with energy 3 eV. The proton captures the electrons and forms a hydrogen atom in second excited state. The resulting photon is incident on a photosensitive metal of threshold wavelength 4000 A. What is the maximum kinetic energy of the emitted photoelectron?

Consider the following statements:
A. Atoms of each element emit characteristics spectrum.
B. According to Bohr's Postulate, an electron in a hydrogen atom revolves in a certain stationary orbit.
C. The density of nuclear matter depends on the size of the nucleus.
D. A free neutron is stable but a free proton decay is possible.
E. Radioactivity is an indication of the instability of nuclei. Choose the correct answer from the options given below.

Find the truth table for the function Y of A and B represented in the following figure.

A swimmer wants to cross a river from point $$A$$ to point $$B$$. Line AB makes an angle of 30° with the flow of the river. The magnitude of the velocity of the swimmer is the same as that of the river. The angle $$\theta$$ with the line AB should be _________ °, so that the swimmer reaches point $$B$$.

A small block slides down from the top of hemisphere of radius $$R = 3$$ m as shown in the figure. The height $$h$$ at which the block will lose contact with the surface of the sphere is _________ m. (Assume there is no friction between the block and the hemisphere)

The water is filled up to a height of 12 m in a tank having vertical sidewalls. A hole is made in one of the walls at a depth $$h$$ below the water level. The value of $$h$$ for which the emerging stream of water strikes the ground at the maximum range is _________ m.

In the given figure, two wheels $$P$$ and $$Q$$ are connected by a belt $$B$$. The radius of $$P$$ is three times that of $$Q$$. In the case of the same rotational kinetic energy, the ratio of rotational inertias $$\left(\frac{I_1}{I_2}\right)$$ will be $$x : 1$$. The value of $$x$$ will be _________.

A particle executes simple harmonic motion represented by displacement function as $$x(t) = A\sin(\omega t + \phi)$$. If the position and velocity of the particle at $$t = 0$$ s are 2 cm and 2$$\omega$$ cm s$$^{-1}$$ respectively, then its amplitude is $$x\sqrt{2}$$ cm where the value of $$x$$ is _________

For the circuit shown, the value of current at time $$t = 3.2$$ s will be _________ A.

[Voltage distribution V(t) is shown by Fig. (1) and the circuit is shown in Fig. (2)]

In the given figure the magnetic flux through the loop increases according to the relation $$\phi_B(t) = 10t^2 + 20t$$, where $$\phi_B$$ is in milliwebers and $$t$$ is in seconds. The magnitude of current through $$R = 2 \, \Omega$$ resistor at $$t = 5$$ s is _________ mA.

The difference in the number of waves when yellow light propagates through air and vacuum columns of the same thickness is one. The thickness of the air column is _________ mm. [Refractive index of air = 1.0003, the wavelength of yellow light in vacuum = 6000 Å]

The $$K_\alpha$$ X-ray of molybdenum has wavelength 0.071 nm. If the energy of a molybdenum atom with a $$K$$ electron knocked out is 27.5 keV, the energy of this atom when an $$L$$ electron is knocked out will be _________ keV. (Round off to the nearest integer) [$$h = 4.14 \times 10^{-15}$$ eV s, $$c = 3 \times 10^8$$ m s$$^{-1}$$]

The maximum amplitude for an amplitude modulated wave is found to be 12 V while the minimum amplitude is found to be 3 V. The modulation index is 0.6$$x$$ where $$x$$ is _________.