A body of mass '$$\mathrm{m}$$' is raised through a height above the earth's surface so that the increase in potential energy is $$\frac{\mathrm{mgR}}{5}$$. The height to which the body is raised is ( $$\mathrm{R}=$$ radius of earth, $$\mathrm{g}=$$ acceleration due to gravity)

With increase in frequency of a.c. supply, the impedance of an L-C-R series circuit

A passenger is sitting in a train which is moving fast. The engine of the train blows a whistle of frequency '$$n$$'. If the apparent frequency of sound heard by the passenger is '$$f$$' then

If the magnitude of intensity of electric field at a distance '$$r_1$$' on an axial line and at a distance '$$r_2$$' on an equatorial line due to a given short dipole are equal, then $$r_1: r_2$$, is