Adsorption of a gas follows the Freundlich adsorption isotherm. $x$ is the mass of the gas adsorbed on mass $m$ of the adsorbent. The plot of $\log(\frac{x}{m})$ versus $\log p$ is shown in the given graph. $\frac{x}{m}$ is proportional to :

If for $x \in \left( 0, \frac{1}{4} \right)$,the derivative of $\tan^{-1} \left( \frac{6x\sqrt{x}}{1 - 9x^3} \right)$ is $\sqrt{x} \cdot g(x)$,then $g(x)$ equals:

Two bar magnets $A$ and $B$ are placed one over the other and are allowed to vibrate in a vibration magnetometer. They make $20$ oscillations per minute when the similar poles of $A$ and $B$ are on the same side,while they make $15$ oscillations per minute when their opposite poles lie on the same side. If $M_A$ and $M_B$ are the magnetic moments of $A$ and $B$ and if $M_A > M_B$,the ratio of $M_A$ and $M_B$ is

The sum of two numbers is $20$. If the product of the square of one number and the cube of the other is maximum,then the numbers are:

The oxidation number of $Pt$ in $[Pt(C_2H_4)Cl_3]^-$ is

The value of $\frac{15}{\sqrt{10} + \sqrt{20} + \sqrt{40} - \sqrt{5} - \sqrt{80}}$ is