A short bar magnet placed with its axis at $30^{\circ}$ with an external field of $800$ $Gauss$, experiences a torque of $0.016 ext{ N.m}$. The work done in moving it from most stable to most unstable position is $\alpha \times 10^{-3} ext{ J}$. The value of $\alpha$ is . . . . . . . . . .

Which of the following hydroxides is acidic?

The solubility of $N_2$ in water at $300 \ K$ and $500 \ torr$ partial pressure is $0.01 \ g \ L^{-1}$. The solubility (in $g \ L^{-1}$) at $750 \ torr$ partial pressure is

If $(x, y, z)$ is an arbitrary point lying on a plane $P$ which passes through the points $(42, 0, 0)$,$(0, 42, 0)$,and $(0, 0, 42)$,then the value of the expression $3 + \frac{x-11}{(y-19)^2(z-12)^2} + \frac{y-19}{(x-11)^2(z-12)^2} + \frac{z-12}{(x-11)^2(y-19)^2} - \frac{x+y+z}{14(x-11)(y-19)(z-12)}$ is:

$A$ sinusoidal voltage of peak value $200\, V$ is connected to a diode and resistor $R$ in the circuit shown so that half-wave rectification occurs. If the forward resistance of the diode is negligible compared to $R$,the $rms$ voltage across $R$ is approximately.....$V$.