If $f: R \rightarrow C$ is defined by $f(x)=e^{2 i x}$ for $x \in R$, then $f$ is (where $C$ denotes the set of all complex numbers)

If $y=A \cos n x+B \sin n x$, then $y_2+n^2 y$ is equal to

$A$ circular disc of radius $R$ is removed from a bigger circular disc of radius $2R$ such that the circumferences of the discs touch. The centre of mass of the new disc is at a distance $\alpha R$ from the centre of the bigger disc. The value of $\alpha$ is

$A$ $10 \ kW$ transmitter emits radio waves of wavelength $500 \ m$. The number of photons emitted per second by the transmitter is of the order of:

The value of $k$ such that the lines $2x - 3y + k = 0$,$3x - 4y - 13 = 0$,and $8x - 11y - 33 = 0$ are concurrent,is

$A$ fixed volume of iron is drawn into a wire of length $L$. The extension $x$ produced in this wire by a constant force $F$ is proportional to