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

Which classification system was proposed by $Woese$?

The eccentricity of the ellipse $x^2+4y^2+2x+16y+13=0$ is

Five capacitors,each of capacitance $C$,are connected as shown in the figure. The ratio of the equivalent capacitance between $P$ and $R$ to the equivalent capacitance between $P$ and $Q$ is:

The period of $\left(\tan \theta - \frac{1}{3} \tan^3 \theta\right) \left(\frac{1}{3} - \tan^2 \theta\right)^{-1}$,where $\tan^2 \theta \neq \frac{1}{3}$,is

$50 \, g$ of ice at $0^{\circ} C$ is dropped into a calorimeter containing $100 \, g$ of water at $30^{\circ} C$. If the thermal capacity of the calorimeter is zero,then the amount of ice left in the mixture at equilibrium is .......... $g$.