NTA JEE Main 25th July 2021 Shift 2

A force of $$F = (5y + 20)\hat{j}$$ N acts on a particle. The work done by this force when the particle is moved from $$y = 0$$ m to $$y = 10$$ m is _________ J.

A solid disc of radius 20 cm and mass 10 kg is rotating with an angular velocity of 600 rpm, about an axis normal to its circular plane and passing through its centre of mass. The retarding torque required to bring the disc at rest in 10 s is _________ $$\pi \times 10^{-1}$$ N m

A system consists of two types of gas molecules $$A$$ and $$B$$ having the same number density $$2 \times 10^{25}$$ m$$^{-3}$$. The diameter of $$A$$ and $$B$$ are 10A and 5A respectively. They suffer collisions at room temperature. The ratio of average distance covered by the molecule $$A$$ to that of $$B$$ between two successive collisions is _________ $$\times 10^{-2}$$

A 16 $$\Omega$$ wire is bent to form a square loop. A 9 V supply having an internal resistance of 1 $$\Omega$$ is connected across one of its sides. The potential drop across the diagonals of the square loop is _________ $$\times 10^{-1}$$ V.

Two circuits are shown in figure (a) and (b). At a frequency of _________ rad s$$^{-1}$$ the average power dissipated in one cycle will be the same in both the circuits.

A light beam of wavelength 500 nm is incident on a metal having work function of 1.25 eV, placed in a magnetic field of intensity $$B$$. The electrons emitted perpendicular to the magnetic field $$B$$, with maximum kinetic energy are bent into a circular arc of radius 30 cm. The value of $$B$$ is _________ $$\times 10^{-7}$$ T.
Given $$hc = 20 \times 10^{-26}$$ J m, the mass of the electron = $$9 \times 10^{-31}$$ kg.

From the given data, the amount of energy required to break the nucleus of aluminium $$_{13}^{27}$$Al is _________ $$x \times 10^{-3}$$ J
Mass of neutron = 1.00866 u
Mass of proton = 1.00726 u
Mass of Aluminium nucleus = 27.18846 u
(Assume 1 u corresponds to $$x$$ J of energy)
(Round off to the nearest integer)

The nuclear activity of a radioactive element becomes $$\left(\frac{1}{8}\right)^{th}$$ of its initial value in 30 years. The half-life of radioactive element is _________ years.

In a semiconductor, the number density of intrinsic charge carriers at 27°C is $$1.5 \times 10^{16}$$ m$$^{-3}$$. If the semiconductor is doped with an impurity atom, the hole density increases to $$4.5 \times 10^{22}$$ m$$^{-3}$$. The electron density in the doped semiconductor is _________ $$\times 10^{9}$$ m$$^{-3}$$

A message signal of frequency 20 kHz and peak voltage of 20 V is used to modulate a carrier wave of frequency 1 MHz and peak voltage of 20 V. The modulation index will be: