The figure shows wave fronts in still water,moving in the direction of the arrow towards the interface $PQ$ between a shallow region and a deep (denser) region. Which of the lines shown may represent one of the wave fronts in the deep region?

$A$ metal nitrate reacts with $KI$ to give a black precipitate which on addition of excess of $KI$ converts into an orange-colored solution. The cation of the metal nitrate is

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).

Nerve cells do not divide because they do not have:

An ideal gas expands isothermally from a volume $V_1$ to $V_2$ and is then compressed to the original volume $V_1$ adiabatically. The initial pressure is $P_1$ and the final pressure is $P_3$. If the total work done is $W$,then:

The distance between the foci of the hyperbola $x^2 - 3y^2 - 4x - 6y - 11 = 0$ is