An open organ pipe and closed organ pipe of same length produce 2 beats per second, when they are set into vibrations together, in fundamental mode. The length of open pipe is made half and that of closed pipe is doubled.

The number of beats produced per second will be (neglect end correction)

A beam of light of intensity $I_0$ falls on a system of three polaroids which are arranged in succession such that the pass (transmission) axis is turned through $60^{\circ}$ with respect to preceding one. The fraction of the incident light intensity that passes through the system is $\left(\cos 60^{\circ}=\frac{1}{2}\right)$

The angular momentum of a rotating body is ' $L$ '. When the frequency of rotating body is tripled and its kinetic energy is made one-third, the new angular momentum becomes

An electric dipole of length 2 cm is placed with its axis making an angle of $60^{\circ}$ to a uniform electric field of $10^{+5} \mathrm{~N} / \mathrm{C}$. If it experiences a torque of $9 \sqrt{3} \mathrm{Nm}$, the magnitude of the charge on the dipole is $\left(\sin 60^{\circ}=\frac{\sqrt{3}}{2}\right)$