NTA JEE Main 24th February 2021 Shift 2

Two solids $$A$$ and $$B$$ of mass 1 kg and 2 kg respectively are moving with equal linear momentum. The ratio of their kinetic energies $$(K.E.)_A : (K.E.)_B$$ will be $$\frac{A}{1}$$, so the value of $$A$$ will be ______.

A uniform thin bar of mass 6 kg and length 2.4 meter is bent to make an equilateral hexagon. The moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of hexagon is ______ $$\times 10^{-1}$$ kg m$$^2$$.

A uniform metallic wire is elongated by 0.04 m when subjected to a linear force $$F$$. The elongation, if its length and diameter is doubled and subjected to the same force will be ______ cm.

The root-mean-square speed of molecules of a given mass of a gas at 27°C and 1 atmosphere pressure is 200 m s$$^{-1}$$. The root-mean-square speed of molecules of the gas at 127°C and 2 atmosphere pressure is $$\frac{x}{\sqrt{3}}$$ m s$$^{-1}$$. The value of $$x$$ will be ______.

Two cars are approaching each other at an equal speed of 7.2 km hr$$^{-1}$$. When they see each other, both blow horns having a frequency of 676 Hz. The beat frequency heard by each driver will be ______ Hz. [Velocity of sound in air is 340 m s$$^{-1}$$.]

A point charge of $$+12$$ $$\mu C$$ is at a distance 6 cm vertically above the centre of a square of side 12 cm as shown in figure. The magnitude of the electric flux through the square will be ______ $$\times 10^3$$ N m$$^2$$ C$$^{-1}$$.

A cylindrical wire of radius 0.5 mm and conductivity $$5 \times 10^7$$ S m$$^{-1}$$ is subjected to an electric field of 10 mV m$$^{-1}$$. The expected value of current in the wire will be $$x^3\pi$$ mA. The value of $$x$$ is ______.

A series LCR circuit is designed to resonate at an angular frequency $$\omega_0 = 10^5$$ rad s$$^{-1}$$. The circuit draws 16 W power from 120 V source at resonance. The value of resistance $$R$$ in the circuit is ______ $$\Omega$$.

An electromagnetic wave of frequency 3 GHz enters a dielectric medium of relative electric permittivity 2.25 from vacuum. The wavelength of this wave in that medium will be ______ $$\times 10^{-2}$$ cm.

A signal of 0.1 kW is transmitted in a cable. The attenuation of cable is $$-5$$ dB per km and cable length is 20 km. The power received at the receiver is $$10^{-x}$$ W. The value of $$x$$ is ______. [Gain in dB = $$10 \log_{10}\left(\frac{P_O}{P_i}\right)$$]