NTA JEE Main 28th July 2022 Shift 1

If the projection of $$2\hat{i} + 4\hat{j} - 2\hat{k}$$ on $$\hat{i} + 2\hat{j} + \alpha\hat{k}$$ is zero. Then, the value of $$\alpha$$ will be

A block of mass 'm' (as shown in figure) moving with kinetic energy E compresses a spring through a distance 25 cm when, its speed is halved. The value of spring constant of used spring will be $$nE$$ N m$$^{-1}$$ for $$n$$ = _____.

Four identical discs each of mass 'M' and diameter 'a' are arranged in a small plane as shown in figure. If the moment of inertia of the system about OO' is $$\frac{x}{4}Ma^2$$. Then, the value of $$x$$ will be _____.

The diameter of an air bubble which was initially 2 mm, rises steadily through a solution of density 1750 kg/m$$^3$$ at the rate of 0.35 cm/s. Coefficient of viscosity of the solution is _____ Poise. (Assume mass of the bubble to be negligible) (Answer in Poise to the nearest integer)

The frequency of echo will be _____ Hz if the train blowing a whistle of frequency 320 Hz is moving with a velocity of 36 km h$$^{-1}$$ towards a hill from which an echo is heard by the train driver. Velocity of sound in air is 330 m s$$^{-1}$$.

Two electric dipoles of dipole moments $$1.2 \times 10^{-30}$$ Cm and $$2.4 \times 10^{-30}$$ Cm are placed in two different uniform electric fields of strengths $$5 \times 10^4$$ N C$$^{-1}$$ and $$15 \times 10^4$$ N C$$^{-1}$$ respectively. The ratio of maximum torque experienced by the electric dipoles will be $$\frac{1}{x}$$. The value of $$x$$ is _____.

As shown in the figure, a potentiometer wire of resistance 20 $$\Omega$$ and length 300 cm is connected with resistance box (R.B.) and a standard cell of emf 4 V. For a resistance 'R' of resistance box introduced into the circuit, the null point for a cell of 20 mV is found to be 60 cm. The value of 'R' is _____ $$\Omega$$.

The frequencies at which the current amplitude in an LCR series circuit becomes $$\frac{1}{\sqrt{2}}$$ times its maximum value, are 212 rad s$$^{-1}$$ and 232 rad s$$^{-1}$$. The value of resistance in the circuit is $$R = 5 \ \Omega$$. The self inductance in the circuit is _____ mH.

In a Young's double slit experiment, a laser light of 560 nm produces an interference pattern with consecutive bright fringes' separation of 7.2 mm. Now another light is used to produce an interference pattern with consecutive bright fringes' separation of 8.1 mm. The wavelength of second light is _____ nm.

A freshly prepared radioactive source of half life 2 hours 30 minutes emits radiation which is 64 times the permissible safe level. The minimum time, after which it would be possible to work safely with source, will be _____ hours.