NTA JEE Main 29th July 2022 Shift 1

An object is projected in the air with initial velocity u at an angle $$\theta$$. The projectile motion is such that the horizontal range R, is maximum. Another object is projected in the air with a horizontal range half of the range of first object. The initial velocity remains same in both the case. The value of the angle of projection, at which the second object is projected, will be _____ degree.

If the acceleration due to gravity experienced by a point mass at a height h above the surface of earth is same as that of the acceleration due to gravity at a depth $$\alpha h$$ ($$ h \ll R_E$$) from the earth surface. The value of $$\alpha$$ will be _____. (use $$R_E = 6400$$ km)

The pressure $$P_1$$ and density $$d_1$$ of diatomic gas $$(\gamma = \frac{7}{5})$$ changes suddenly to $$P_2(> P_1)$$ and $$d_2$$ respectively during an adiabatic process. The temperature of the gas increases and becomes _____ times of its initial temperature. (Given $$\frac{d_2}{d_1} = 32$$)

One mole of a monoatomic gas is mixed with three moles of a diatomic gas. The molecular specific heat of mixture at constant volume is $$\frac{\alpha^2}{4}R$$ J mol$$^{-1}$$ K$$^{-1}$$; then the value of $$\alpha$$ will be _____. (Assume that the given diatomic gas has no vibrational mode.)

Two light beams of intensities 4I and 9I interfere on a screen. The phase difference between these beams on the screen at point A is zero and at point B is $$\pi$$. The difference of resultant intensities, at the point A and B, will be _____ I.

The current I flowing through the given circuit will be _____ A.

A closely wound circular coil of radius 5 cm produces a magnetic field of $$37.68 \times 10^{-4}$$ T at its center. The current through the coil is _____ A. [Given, number of turns in the coil is 100 and $$\pi = 3.14$$]

A wire of length 314 cm carrying current of 14 A is bent to form a circle. The magnetic moment of the coil is _____ A-m$$^2$$. [Given $$\pi = 3.14$$]

The X-Y plane be taken as the boundary between two transparent media $$M_1$$ and $$M_2$$. $$M_1$$ in $$Z \geq 0$$ has a refractive index of $$\sqrt{2}$$ and $$M_2$$ with $$Z < 0$$ has a refractive index of $$\sqrt{3}$$. A ray of light travelling in $$M_1$$ along the direction given by the vector $$\vec{A} = 4\sqrt{3}\hat{i} - 3\sqrt{3}\hat{j} - 5\hat{k}$$, is incident on the plane of separation. The value of difference between the angle of incident in $$M_1$$ and the angle of refraction in $$M_2$$ will be _____ degree.

If the potential barrier across a p-n junction is 0.6 V. Then the electric field intensity, in the depletion region having the width of $$6 \times 10^{-6}$$ m, will be _____ $$\times 10^5$$ N C$$^{-1}$$