Which one of the following metallic hydroxides does not dissolve in sodium hydroxide solution?

$A$ coil of wire of radius $r$ has $600$ turns and a self-inductance of $108 \ mH$. The self-inductance of a coil with the same radius and $500$ turns is (in $mH$)

Two wires of the same material have lengths in the ratio $1:2$ and their radii are in the ratio $1:\sqrt{2}$. If they are stretched by applying equal forces,the increase in their lengths will be in the ratio:

An organ pipe $P_1$,closed at one end and containing a gas of density $\rho_1$ is vibrating in its first harmonic. Another organ pipe $P_2$,open at both ends and containing a gas of density $\rho_2$ is vibrating in its third harmonic. Both the pipes are in resonance with a given tuning fork. If the compressibility of gases is equal in both pipes,the ratio of the lengths of $P_1$ and $P_2$ is (assume the given gases to be monoatomic).

If two angles of $\triangle ABC$ are $45^{\circ}$ and $60^{\circ}$,then the ratio of the smallest side to the greatest side is:

If $\tanh ^{-1} x = a \log \left(\frac{1+x}{1-x}\right)$,$|x| < 1$,then $a$ is equal to