The height at which the weight of the body becomes $$\left(\frac{1}{9}\right)^{\text {th }}$$ its weight on the surface of earth is $$(\mathrm{R}=$$ radius of earth)

A single turn current loop in the shape of a right angle triangle with side $$5 \mathrm{~cm}, 12 \mathrm{~cm}, 13 \mathrm{~cm}$$ is carrying a current of $$2 \mathrm{~A}$$. The loop is in a uniform magnetic field of magnitude $$0.75 \mathrm{~T}$$ whose direction is parallel to the current in the $$13 \mathrm{~cm}$$ side of the loop. The magnitude of the magnetic force on the $$5 \mathrm{~cm}$$ side will be $$\frac{\mathrm{x}}{130} \mathrm{~N}$$. The value of '$$x$$' is

41 tuning forks are arranged in increasing order of frequency such that each produces 5 beats/second with next tuning fork. If frequency of last tuning fork is double that of frequency of first fork. Then frequency of first and last fork is

In two separate setups for Biprism experiment using same wavelength, fringes of equal width are obtained. If ratio of slit separation is $$2: 3$$ then the ratio of the distance between the slit and screen in the two setups is