$A$ Zener diode,having a breakdown voltage equal to $15 \, V$,is used in a voltage regulator circuit as shown in the figure. The current through the diode is ..... $mA$.

The solution of the differential equation $\frac{dy}{dx} = \frac{y}{x} + \frac{\phi(y/x)}{\phi'(y/x)}$ is

The equation of the line passing through the point of intersection of the lines $x-3y+2=0$ and $2x+5y-7=0$ and perpendicular to the line $3x+2y+5=0$ is:

In which of the following arrangements,the order is $NOT$ according to the property indicated against it?

Two metal wires of identical dimensions are connected in series. If $\sigma_{1}$ and $\sigma_{2}$ are the electrical conductivities of the metal wires respectively, the effective conductivity of the combination is

The r.m.s. velocity of $CO_2$ at a temperature $T$ (in kelvin) is $x \ cm \ s^{-1}$. At what temperature (in kelvin),the r.m.s. velocity of nitrous oxide would be $4 x \ cm \ s^{-1}$ (in $T$)? (Atomic weights of $C, N$ and $O$ are respectively $12, 14$ and $16$)