Cinnabar is mercury(II) sulphide, \(\mathrm{HgS}\). On roasting in air it yields mercury metal.
Overall reaction (roasting):
\[ \mathrm{HgS \;+\; O_2 \;\longrightarrow\; Hg \;+\; SO_2} \]
Stepwise (often shown in textbooks):
\[ \mathrm{2\,HgS \;+\; 3\,O_2 \;\longrightarrow\; 2\,HgO \;+\; 2\,SO_2} \] \[ \mathrm{2\,HgO \;\xrightarrow{\Delta}\; 2\,Hg \;+\; O_2} \] (Mercury vapour condensed to liquid mercury.)
Find the unknown frequency if 24 is the median of the following frequency distribution:
\[\begin{array}{|c|c|c|c|c|c|} \hline \text{Class-interval} & 0-10 & 10-20 & 20-30 & 30-40 & 40-50 \\ \hline \text{Frequency} & 5 & 25 & 25 & \text{$p$} & 7 \\ \hline \end{array}\]
Two concentric circles are of radii $8\ \text{cm}$ and $5\ \text{cm}$. Find the length of the chord of the larger circle which touches (is tangent to) the smaller circle.