NTA JEE Main 8 April 2018 Offline

An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii $$r_e$$, $$r_p$$, $$r_\alpha$$ respectively in a uniform magnetic field B. The relation between $$r_e$$, $$r_p$$, $$r_\alpha$$ is:

For an RLC circuit driven with voltage of amplitude $$v_m$$ and frequency $$\omega_0 = \frac{1}{\sqrt{LC}}$$, the current exhibits resonance. The quality factor, Q is given by:

In an A.C. circuit, the instantaneous e.m.f. and current are given by, $$E = 100 \sin 30t$$, $$I = 20 \sin\left(30t - \frac{\pi}{4}\right)$$. In one cycle of A.C., the average power consumed by the circuit (in watt) and the watt-less current (in ampere) are, respectively:

An EM wave from air enters a medium. The electric fields are $$\vec{E_1} = E_{01}\hat{x}\cos\left[2\pi\nu\left(\frac{z}{c} - t\right)\right]$$ in air and $$\vec{E_2} = E_{02}\hat{x}\cos[k(2z - ct)]$$ in medium, where the wave number k and frequency $$\nu$$ refer to their values in the air. The medium is non-magnetic. If $$\epsilon_{r_1}$$ and $$\epsilon_{r_2}$$ refer to relative permittivities of air and medium respectively, which of the following options is correct?

Unpolarized light of intensity I passes through an ideal polariser A. Another identical polariser B is placed behind A. The intensity of light beyond B is found to be $$\frac{I}{2}$$. Now another identical polariser C is placed between A and B. The intensity beyond B is now found to be $$\frac{I}{8}$$. The angle between polariser A and C is:

The angular width of the central maximum in a single slit diffraction pattern is 60$$^\circ$$. The width of the slit is 1 $$\mu$$m. The slit is illuminated by monochromatic plane waves. If another slit of the same width is made near it, Young's fringes can be observed on a screen placed at a distance 50 cm from the slits. If the observed fringe width is 1 cm, what is slit separation distance? (i.e., the distance between the centres of each slit.)

An electron from various excited states of hydrogen atom emit radiation to come to the ground state. Let $$\lambda_n$$, $$\lambda_g$$ be the de Broglie wavelength of the electron in the $$n^{th}$$ state and the ground state respectively. Let $$\Lambda_n$$ be the wavelength of the emitted photon in the transition from the $$n^{th}$$ state to the ground state. For large n, (A, B are constants)

If the series limit frequency of the Lyman series is $$V_L$$, then the series limit frequency of the Pfund series is:

The reading of the ammeter for a silicon diode in the given circuit is:

A telephonic communication service is working at a carrier frequency of 10 GHz. Only 10% of it is utilized for transmission. How many telephonic channels can be transmitted simultaneously if each channel requires a bandwidth of 5 kHz?