(a) Propanal
Condensed structure: \[ \mathrm{CH_3{-}CH_2{-}CHO} \]
(b) 2-Methyl pentanoic acid
Condensed structure: \[ \mathrm{CH_3{-}CH(CH_3){-}CH_2{-}CH_2{-}COOH} \] (Numbering from the –COOH carbon: the methyl is at C-2.)
(c) Propene
Condensed structure: \[ \mathrm{CH_2{=}CH{-}CH_3} \]
(d) 2-Methyl butan-2-ol (often written as 2-methyl-2-butanol)
Condensed structure: \[ \mathrm{(CH_3)_2C(OH){-}CH_2{-}CH_3} \] (–OH and a methyl substituent both at C-2.)
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.