The frequency of the output signal of an LC oscillator circuit is '$$\mathrm{F}$$' Hz with a capacitance of 0.1 $$\mu \mathrm{F}$$. If the value of the capacitor is increased to $$0.2~ \mu \mathrm{F}$$, then the frequency of the output signal will be

A solid sphere of mass '$$M$$' and radius '$$R$$' is rotating about its diameter. A solid cylinder of same mass and same radius is also rotating about its geometrical axis with an angular speet twice that of the sphere. The ratio of the kinetic energy of rotation of the sphere to that of the cylinder is

When a battery is connected to the two ends of a diagonal of a square conductor frame of side '$$a$$', the magnitude of magnetic field at the centre will be ( $$\mu_0=$$ permeability of free space)

A car of mass '$$m$$' moving with velocity '$$u$$' on a straight road in a straight line, doubles its velocity in time t. The power delivered by the engine of a car for doubling the velocity is