Write IUPAC names of the following compounds:
(a) \( \mathrm{CH_2=CH-CH_2Cl} \)
Answer: 3-chloroprop-1-ene
Lowest locant is given to the double bond (ene). Numbering from the alkene end makes the double bond at C-1 and places chloro at C-3.
(b) \( \mathrm{CH_3-CH(OH)-COOH} \)
Answer: 2-hydroxypropanoic acid
Parent acid: propanoic acid (\(\mathrm{COOH}\) has highest priority). The hydroxyl substituent is at C-2. (Common name: lactic acid.)
(c) A three-carbon chain \( \mathrm{CH_2-CH-CH_2} \) with an ethyl group on each carbon.
Answer: 4-ethylheptane
Choose the longest chain passing from left ethyl → \( \mathrm{CH_2-CH-CH_2} \) → right ethyl: this gives a 7-carbon parent (heptane). The remaining ethyl becomes a substituent at the central carbon (C-4) → 4-ethylheptane.
(d) .
Answer: bromochloroiodomethane
Single-carbon parent: methane. Three halo substituents are listed in alphabetical order: bromo, chloro, iodo. (Locants are all 1; writing 1-bromo-1-chloro-1-iodomethane is acceptable.)
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.