Two sounding sources send waves at certain temperature in air of wavelength $$50 \mathrm{~cm}$$ and $$50.5 \mathrm{~cm}$$ respectively. The frequency of sources differ by $$6 \mathrm{~Hz}$$. The velocity of sound in air at same temperature is

In the given circuit, r.m.s. value of current through the resistor $$\mathrm{R}$$ is

A particle of mass '$$m$$' moving east ward with a speed '$$v$$' collides with another particle of same mass moving north-ward with same speed '$$v$$'. The two particles coalesce after collision. The new particle of mass '$$2 \mathrm{~m}$$' will move in north east direction with a speed (in $$\mathrm{m} / \mathrm{s}$$ )

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)