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$1-Methylcyclohexene$ $\xrightarrow[\text{cold}]{alkaline\,KMnO_4} A$ $\xrightarrow[CH_3COOH]{CrO_3} B$
$A$ and $B$ are

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The conversion of $2-$methylpropan$-1-$ol to $2-$methylpropan$-2-$ol is:

The product formed when glycerol reacts with $PCl_5$ is -

What is Lucas reagent?

What are $X$ and $Y$ in the following reactions?
$R-CH_2OH \xrightarrow{Cu/573 \ K} X$
$(CH_3)_3C-OH \xrightarrow{Cu/573 \ K} Y$

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