You are required to design an air-filled solenoid of inductance 0.016 H having a length 0.81 m and radius 0.02 m . The number of turns in the solenoid should be

A voltage $v=v_0 \sin \omega t$ applied to a circuit drives a current $i=i_0 \sin (\omega t+\phi)$ in the circuit. The average power consumed in the circuit over a cycle is

The given diagram exhibits the relationship between the wavelength of the electromagnetic waves and the energy of photon associated with them. The three points $\mathbf{P}, \mathbf{Q}$ and $\mathbf{R}$ marked on the diagram may correspond respectively to

A beaker is filled with water (refractive index $\frac{4}{3}$ ) up to a height $H$. A coin is placed at its bottom. The depth of the coin, when viewed along the near ${ }^n$ ormal direction, will be