NTA JEE Main 26th June 2022 Shift 1

A ball of mass $$0.5$$ kg is dropped from the height of $$10$$ m. The height, at which the magnitude of velocity becomes equal to the magnitude of acceleration due to gravity, is ______ m. [Use $$g = 10$$ m s$$^{-2}$$]

A fighter jet is flying horizontally at a certain altitude with a speed of $$200$$ m s$$^{-1}$$. When it passes directly overhead an anti-aircraft gun, a bullet is fired from the gun, at an angle $$\theta$$ with the horizontal, to hit the jet. If the bullet speed is $$400$$ m s$$^{-1}$$, the value of $$\theta$$ will be ______ °.

The elongation of a wire on the surface of the earth is $$10^{-4}$$ m. The same wire of same dimensions is elongated by $$6 \times 10^{-5}$$ m on another planet. The acceleration due to gravity on the planet will be ______ m s$$^{-2}$$. (Take acceleration due to gravity on the surface of earth $$= 10$$ m s$$^{-2}$$)

The elastic behaviour of material for linear stress and linear strain, is shown in the figure. The energy density for a linear strain of $$5 \times 10^{-4}$$ is ______ kJ m$$^{-3}$$. Assume that material is elastic upto the linear strain of $$5 \times 10^{-4}$$.

An ideal fluid of density $$800$$ kg m$$^{-3}$$, flows smoothly through a bent pipe (as shown in the figure) that tapers in cross-sectional area from $$a$$ to $$\frac{a}{2}$$. The pressure difference between the wide and narrow sections of pipe is $$4100$$ Pa. At the wider section, the velocity of the fluid is $$\frac{\sqrt{x}}{6}$$ m s$$^{-1}$$ for $$x =$$ ______. (Given $$g = 10$$ m s$$^{-2}$$)

A $$10$$ $$\Omega$$, $$20$$ mH coil carrying constant current is connected to a battery of $$20$$ V through a switch. Now after switch is opened current becomes zero in $$100$$ $$\mu$$s. The average e.m.f. induced in the coil is ______ V.

A $$110$$ V, $$50$$ Hz, AC source is connected in the circuit (as shown in figure). The current through the resistance $$55$$ $$\Omega$$, at resonance in the circuit, will be ______ A.

A light ray is incident, at an incident angle $$\theta_1$$, on the system of two plane mirrors $$M_1$$ and $$M_2$$ having an inclination angle $$75°$$ between them (as shown in figure). After reflecting from mirror $$M_1$$ it gets reflected back by the mirror $$M_2$$ with an angle of reflection $$30°$$. The total deviation of the ray will be ______ degree.

As per the given circuit, the value of current through the battery will be ______ A.

In a vernier callipers, each cm on the main scale is divided into $$20$$ equal parts. If tenth vernier scale division coincides with nineth main scale division. Then the value of vernier constant will be ______ $$\times 10^{-2}$$ mm