Two cities $X$ and $Y$ are connected by a regular bus service with a bus leaving in either direction every $T$ min. A girl is driving scooty with a speed of $60 \mathrm{~km} / \mathrm{h}$ in the direction $X$ to $Y$ notices that a bus goes past her every 30 minutes in the direction of her motion, and every 10 minutes in the opposite direction. Choose the correct option for the period $T$ of the bus service and the speed (assumed constant) of the buses.

A container has two chambers of volumes $V_1=2$ litres and $V_2=3$ litres separated by a partition made of a thermal insulator. The chambers contain $n_1=5$ and $n_2=4$ moles of ideal gas at pressures $p_1=1 \mathrm{~atm}$ and $p_2=2 \mathrm{~atm}$, respectively. When the partition is removed, the mixture attains an equilibrium pressure of

De-Broglie wavelength of an electron orbiting in the $n=2$ state of hydrogen atom is close to

(Given Bohr radius $=0.052 \mathrm{~nm}$ )

To an ac power supply of 220 V at 50 Hz , a resistor of $20 \Omega$, a capacitor of reactance $25 \Omega$ and an inductor of reactance $45 \Omega$ are connected in series. The corresponding current in the circuit and the phase angle between the current and the voltage is, respectively