NTA JEE Main 29th July 2022 Shift 1

A spherically symmetric charge distribution is considered with charge density varying as $$\rho(r) = \begin{cases} \rho_0\left(\frac{3}{4} - \frac{r}{R}\right) & \text{for } r \leq R \\ 0 & \text{for } r > R \end{cases}$$
Where, $$r(r < R)$$ is the distance from the centre O (as shown in figure). The electric field at point P will be:

Given below are two statements.
Statement I: Electric potential is constant within and at the surface of each conductor.
Statement II: Electric field just outside a charged conductor is perpendicular to the surface of the conductor at every point.
In the light of the above statements, choose the most appropriate answer from the options given below.

An alternating emf $$E = 440\sin 100\pi t$$ is applied to a circuit containing an inductance of $$\frac{\sqrt{2}}{\pi}$$ H. If an a.c. ammeter is connected in the circuit, its reading will be:

A coil of inductance 1 H and resistance 100 $$\Omega$$ is connected to a battery of 6 V. Determine approximately:
(a) The time elapsed before the current acquires half of its steady-state value
(b) The energy stored in the magnetic field associated with the coil at an instant 15 ms after the circuit is switched on.
(Given $$\ln 2 = 0.693$$, $$e^{-3/2} = 0.25$$)

Match List-I with List-II

Choose the correct answer from the options given below :

The kinetic energy of emitted electron is E when the light incident on the metal has wavelength $$\lambda$$. To double the kinetic energy, the incident light must have wavelength:

Find the ratio of energies of photons produced due to transition of an electron of hydrogen atom from its (i) second permitted energy level to the first level, and (ii) the highest permitted energy level to the first permitted level.

Find the modulation index of an AM wave having 8 V variation where maximum amplitude of the AM wave is 9 V.

A travelling microscope has 20 divisions per cm on the main scale while its Vernier scale has total 50 divisions and 25 Vernier scale divisions are equal to 24 main scale divisions, what is the least count of the travelling microscope?

In an experiment to find out the diameter of wire using screw gauge, the following observation were noted:
(a) Screw moves 0.5 mm on main scale in one complete rotation
(b) Total divisions on circular scale = 50
(c) Main scale reading is 2.5 mm
(d) 45th division of circular scale is in the pitch line
(e) Instrument has 0.03 mm negative error
Then the diameter of wire is: