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(D) The molecular formula for a ketone is $C_nH_{2n}O$. Given $MW = 100$,we have $12n + 2n + 16 = 100$,which gives $14n = 84$,so $n = 6$. The formula

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$5$

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(D) The molecular formula for a ketone is $C_nH_{2n}O$. Given $MW = 100$,we have $12n + 2n + 16 = 100$,which gives $14n = 84$,so $n = 6$. The formula is $C_6H_{12}O$.The possible isomeric ketones are:$1$. $Hexan-2-one$: Reduction gives a chiral alcohol,forming a racemic mixture.$2$. $Hexan-3-one$: Reduction gives a chiral alcohol,forming a racemic mixture.$3$. $4-Methylpentan-2-one$: Reduction gives a chiral alcohol,forming a racemic mixture.$4$. $3-Methylpentan-2-one$: This has a chiral center. Reduction creates a new chiral center,resulting in diastereomers,not a racemic mixture.$5$. $3,3-Dimethylbutan-2-one$: Reduction gives a chiral alcohol,forming a racemic mixture.$6$. $3-Methylpentan-3-one$: Reduction gives a chiral alcohol,forming a racemic mixture.Out of these,$5$ ketones produce a racemic mixture upon reduction with $NaBH_4$.

Consider all possible isomeric ketones,including stereoisomers of $MW = 100$. All these isomers are independently reacted with $NaBH_4$ ($NOTE$: stereoisomers are also reacted separately). The total number of ketones that give a racemic product$(s)$ is/are

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