AIPMT 2012 Preliminary Mock Test

Electron in hydrogen atom first jumps from third excited state to second excited state and then from second excited to the first excited state. The ratio of the wavelengths ${\lambda }_1:{\lambda }_2$ emitted in the two cases is:

The electric field associated with an e.m. wave in vacuum is given by $E=40\cos (kz-6\times 10^{8}t)\hat{i}$. The value of wave vector $k$ is:

An alternating electric field, of frequency $\nu$, is applied across the dees (radius $=R$) of a cyclotron that is being used to accelerate protons (mass $=m$). The operating magnetic field ($B$) used in the cyclotron and the kinetic energy ($K$) of the proton beam are:

The current ($I$) in the inductance is varying with time according to the plot shown. Which one is the correct variation of voltage with time in the coil?

In an electrical circuit $R,L,C$ and an a.c voltage source are all connected in series. When $L$ is removed, the phase difference is $\pi /3$. If instead $C$ is removed, the phase difference is again $\pi /3$. The power factor of the circuit is: