A person observes two moving trains. First reaching the station and another leaves the station with equal speed of $30 \mathrm{~m} / \mathrm{s}$. If both trains emit sounds of frequency 300 Hz , difference of frequencies heard by the person will be (speed of sound in air $330 \mathrm{~m} / \mathrm{s}$ )

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 $\left(\cos 60^{\circ}=\frac{1}{2}\right)$