The foci of the ellipse $\frac{x^2}{16} + \frac{y^2}{b^2} = 1$ and the hyperbola $\frac{x^2}{144} - \frac{y^2}{81} = \frac{1}{25}$ coincide. Then the value of $b^2$ is

Which property among the following is the same for both hydrogen and deuterium molecules?

$\lim _{x \rightarrow 0} \frac{\sin x \sin ^{-1} x}{x^2}$ is equal to

Molar volume $( V_m )$ of a van der Waals gas can be calculated by expressing the van der Waals equation as a cubic equation with $V_m$ as the variable. The ratio $($in $mol dm ^{-3} )$ of the coefficient of $V_m^2$ to the coefficient of $V_m$ for a gas having van der Waals constants $a=6.0 dm ^6 atm \ mol ^{-2}$ and $b=0.060 dm ^3 mol^{-1}$ at $300 K$ and $300 atm$ is $....$ .
Use: Universal gas constant $(R)=0.082 dm ^3 atm \ mol { }^{-1} K^{-1}$

The angle between the lines represented by $y^2 \sin^2 \theta - xy \sin^2 \theta + x^2(\cos^2 \theta - 1) = 0$ is

The density $($in $g cm ^{-3} )$ of the metal which forms a cubic close packed $(ccp)$ lattice with an axial distance $($edge length$)$ equal to $400 \ pm$ is $....$
Use: Atomic mass of metal $=105.6 \ amu$ and Avogadro's constant $=6 \times 10^{23} mol^{-1}$