If $\frac{4 + 3\sqrt{3}}{\sqrt{7 + 4\sqrt{3}}} = a + \sqrt{b}$,then $(a, b) = $

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).

Why does molten sodium chloride conduct electricity?

The number of unpaired electrons in a chromic ion $Cr^{3+}$ (atomic number $= 24$) is

$A$ variable plane passes through a fixed point $(1, 2, 3)$. The foot of the perpendicular from the origin to the plane lies on:

The differential equation of the family $y=a e^x+b x e^x+c x^2 e^x$ of curves,where $a, b, c$ are arbitrary constants,is