A galvanometer has a resistance of $50 ~\Omega$ and it allows maximum current of $5 \mathrm{~mA}$. It can be converted into voltmeter to measure upto $100 \mathrm{~V}$ by connecting in series a resistor of resistance :

The minimum energy required by a hydrogen atom in ground state to emit radiation in Balmer series is nearly :

A parallel plate capacitor has a capacitance $\mathrm{C}=200~ \mathrm{pF}$. It is connected to $230 \mathrm{~V}$ ac supply with an angular frequency $300~ \mathrm{rad} / \mathrm{s}$. The rms value of conduction current in the circuit and displacement current in the capacitor respectively are :

The de Broglie wavelengths of a proton and an $\alpha$ particle are $\lambda$ and $2 \lambda$ respectively. The ratio of the velocities of proton and $\alpha$ particle will be :