$A$ 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 Zener diode is $.....\ mA$.

The force $\vec{F} = 7\widehat{i} + 3\widehat{j} - 5\widehat{k}$ acts on a particle whose position vector is $\vec{r} = \widehat{i} - \widehat{j} + \widehat{k}$. What is the torque of the given force about the origin?

$A$ vessel contains $1$ mole of $O_2$ gas (molar mass $32$) at a temperature $T$. The pressure of the gas is $P$. An identical vessel containing $1$ mole of $He$ gas (molar mass $4$) at a temperature $2T$ has a pressure of:

The angle between the asymptotes of the hyperbola $x^2-3y^2=3$ is

The inverse of the matrix $\left[\begin{array}{ccc}7 & -3 & -3 \\ -1 & 1 & 0 \\ -1 & 0 & 1\end{array}\right]$ is

$A$ car is moving with a speed of $72 ~km/h$ towards a hill. The car blows its horn at a distance of $1800 ~m$ from the hill. If the echo is heard after $10 ~s$,what is the speed of sound in $m/s$?