b
since '\(A\)' gives positive silver mirror test therefore, it must be an aldehyde or \(\alpha\) -Hydroxyketone.

Reaction with semicarbazide indicates that \(A\) can be an aldehyde or ketone.

Reaction with \(O H^{-}\) i.e., aldol condensation (by assuming alkali to be dilute) indicates that \(A\) is aldehyde as aldol reaction of ketones is reversible and carried out in special apparatus.

\(\mathop {C{H_3} - C{H_2}OH}\limits_{(X)} \xrightarrow[{573\,\,K}]{{Cu}}\) \(\mathop {C{H_3} - CHO}\limits_{(A)} \xrightarrow[\Delta ]{{{{[Ag{{(N{H_3})}_2}]}^ + }\,,\,O{H^ - }}}\) \(C{H_3} - COOH\)

\(\mathop {\mathop {C{H_3} - CHO}\limits_{(A)} }\limits_{ethanal} \xrightarrow{{\begin{array}{*{20}{c}}
  {\,\,\,\,\,\,\,\,\,\,\,\,\,O} \\ 
  {\,\,\,\,\,\,\,\,\,\,\,\,||} \\ 
  {{H_2}N - NH - C - N{H_2}} 
\end{array}}}\) \(\begin{array}{*{20}{c}}
  {\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,O} \\ 
  {\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,||} \\ 
  {\mathop {C{H_3} - CH = }\limits_{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(Z)} N - NH - C - N{H_2}} 
\end{array}\)

\(\mathop {\mathop {C{H_3} - CHO}\limits_{(A)} }\limits_{ethanal} \) \(\xrightarrow{{O{H^ - }}}\) \(\mathop {\begin{array}{*{20}{c}}
  {OH\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,} \\ 
  {|\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,} \\ 
  {C{H_3} - CH - C{H_2} - CHO} 
\end{array}}\limits_{3\, - \,Hydroxybutanal} \) \(\xrightarrow{\Delta }\) \(\underset{\begin{smallmatrix} 
 (Y) \\ 
 But\,-\,2\,\,-\,enal 
\end{smallmatrix}}{\mathop{C{{H}_{3}}-CH=CH-CHO}}\,\)