NTA JEE Main 24th June 2022 Shift 2

A body is projected from the ground at an angle of $$45°$$ with the horizontal. Its velocity after $$2$$ s is $$20$$ m s$$^{-1}$$. The maximum height reached by the body during its motion is ______ m. (use $$g = 10$$ m s$$^{-2}$$)

In an experiment to verify Newton's law of cooling, a graph is plotted between the temperature difference $$(\Delta T)$$ of the water and surroundings and time as shown in figure. The initial temperature of water is taken as $$80°$$C. The value of $$t_2$$ as mentioned in the graph will be ______

A monoatomic gas performs a work of $$\frac{Q}{4}$$ where $$Q$$ is the heat supplied to it. The molar heat capacity of the gas will be ______ $$R$$.
Where $$R$$ is the gas constant.

Two travelling waves of equal amplitudes and equal frequencies move in opposite directions along a string. They interfere to produce a stationary wave whose equation is given by $$y = \left(10 \cos \pi x \sin \frac{2\pi t}{T}\right)$$ cm. The amplitude of the particle at $$x = \frac{4}{3}$$ cm will be ______ cm.

A potentiometer wire of length $$10$$ m and resistance $$20$$ $$\Omega$$ is connected in series with a $$25$$ V battery and an external resistance $$30$$ $$\Omega$$. A cell of emf $$E$$ in secondary circuit is balanced by $$250$$ cm long potentiometer wire. The value of $$E$$ (in volt) is $$\frac{x}{10}$$. The value of $$x$$ is ______.

A circular coil of $$1000$$ turns each with area $$1$$ m$$^2$$ is rotated about its vertical diameter at the rate of one revolution per second in a uniform horizontal magnetic field of $$0.07$$ T. The maximum voltage generation will be ______ V.

A ray of light is incident at an angle of incidence $$60°$$ on the glass slab of refractive index $$\sqrt{3}$$. After refraction, the light ray emerges out from other parallel faces and lateral shift between incident ray and emergent ray is $$4\sqrt{3}$$ cm. The thickness of the glass slab is ______ cm.

A sample contains $$10^{-2}$$ kg each of two substances $$A$$ and $$B$$ with half lives $$4$$ s and $$8$$ s respectively. The ratio of their atomic weights is $$1 : 2$$. The ratio of the amounts of $$A$$ and $$B$$ after $$16$$ s is $$\frac{x}{100}$$. The value of $$x$$ is ______.

In the given circuit, the value of current $$I_L$$ will be ______ mA. (When $$R_L = 1$$ k$$\Omega$$)

An antenna is placed in a dielectric medium of dielectric constant $$6.25$$. If the maximum size of that antenna is $$5.0$$ mm, it can radiate a signal of minimum frequency of ______ GHz.
(Given $$\mu_r = 1$$ for dielectric medium)