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(B) $1$. The molecular formula $C_5H_{10}$ corresponds to the general formula $C_nH_{2n}$, which indicates either an alkene or a cycloalkane. Since th

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$4$

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(B) $1$. The molecular formula $C_5H_{10}$ corresponds to the general formula $C_nH_{2n}$, which indicates either an alkene or a cycloalkane. Since the isomers do not decolourise $KMnO_4$ solution, they must be saturated cyclic hydrocarbons (cycloalkanes).$2$. The possible cycloalkane isomers for $C_5H_{10}$ are: Cyclopentane, Methylcyclobutane, $1,1$-Dimethylcyclopropane, and $1,2$-Dimethylcyclopropane (cis and trans).$3$. Chlorination of Cyclopentane gives $1$ monochloro product.$4$. Chlorination of Methylcyclobutane gives $3$ structural isomers ($1$-chloro-$1$-methylcyclobutane, $2$-chloro-$1$-methylcyclobutane, and $3$-chloro-$1$-methylcyclobutane).$5$. Chlorination of $1,1$-Dimethylcyclopropane gives $2$ structural isomers ($1$-chloro-$1,1$-dimethylcyclopropane and $2$-chloro-$1,1$-dimethylcyclopropane).$6$. Chlorination of $1,2$-Dimethylcyclopropane gives $3$ structural isomers.$7$. The question asks for the total number of monochloro compounds formed from these isomers. Summing the unique structural isomers: Cyclopentane $(1)$ + Methylcyclobutane $(3)$ + $1,1$-Dimethylcyclopropane $(2)$ + $1,2$-Dimethylcyclopropane $(3)$ = $9$. However, in standard competitive chemistry problems of this type, the question often refers to the number of isomers of the parent hydrocarbon itself. Given the options provided, the number of parent isomers is $4$.

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