Two parallel plate air capacitors of same capacity ' C ' are connected in series to a battery of emf ' $E$ '. Then one of the capacitors is completely filled with dielectric material of constant ' K '. The change in the effective capacity of the series combination is

Assuming that the earth is revolving around the sun in circular orbit of radius R , the angular momentum is directly proportional to $\mathrm{R}^{\mathrm{n}}$. The value of ' $n$ ' is

With what velocity an observer should move relative to a stationary source so that a sound of triple the frequency of source is heard by an observer?

Two long straight parallel wires are separated by a distance '2d'. Each wire carries a current 'I' in the same direction. The magnetic field at a point 'P' midway between them is