(c)
Since, the compound ‘B’ gave a 2,4-dinitrophenylhydrazine derivative but did not answer halogen test or silver mirror test, it must contains a >C=O group, but it is neither a methyl ketone nor an aldehyde.
Moreover, compound ‘B’ is obtained by the oxidation of compound ‘A’ having molecular formula$C_{5}H_{12}O$, so the compound must be a secondary alcohol.
$CH_{3} - CH_{2}CH - CH_{2} - CH_{3}\underset{- H_{2}O}{\overset{\ \ \ \ \ \ \lbrack O\rbrack\ \ \ \ }{\rightarrow}}$
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OH
2^{0} alcohol
(Compound ‘A’)
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ CH_{3} - CH_{2}C - CH_{2} - CH_{3}$
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$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ O\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \$
Ketone
(Compound ‘B’)