A tuning fork vibrates with frequency $$256$$ $$Hz$$ and gives one beat per second with the third normal mode of vibration of an open pipe. What is the length of the pipe ? (Speed of sound in air is $$340\,m{s^{ - 1}}$$)

A Helmholtz coil has a pair of loops, each with $$N$$ turns and radius $$R$$. They are placed coaxially at distance $$R$$ and the same current $${\rm I}$$ flows through the loops in the same direction. $$P,$$ midway between the centers $$A$$ and $$C$$, is given by [Refer to figure given below] :

Light of wavelength $$550$$ $$nm$$ falls normally on a slit of width $$22.0 \times {10^{ - 5}}$$ $$cm.$$ The angular position of the second minima from the central maximum will (in radians) :

A monochromatic beam of light has a frequency $$v = {3 \over {2\pi }} \times {10^{12}}Hz$$ and is propagating along the direction $${{\widehat i + \widehat j} \over {\sqrt 2 }}.$$
It is polarized along the $$\widehat k$$ direction. The acceptable form for the magnetic field is :