The correct acidity order of the following compounds is:

Increasing order of boiling points in the following compounds is:
$I$. $CH_3COOH$
$II$. $CH_3CH_2CHO$
$III$. $CH_3CH_2CH_2OH$
$IV$. $CH_3COCH_3$

$A$ $\xrightarrow[\text{(ii) } H_3O^{+}]{\text{(i) } NaOH} B$ $\xrightarrow[\text{(ii) } H_2SO_4, \Delta]{\text{(i) } EtOH} C$
'$A$' shows positive Lassaigne's test for $N$ and its molar mass is $121$.
'$B$' gives effervescence with aq. $NaHCO_3$.
'$C$' gives fruity smell.
Identify $A, B$ and $C$ from the following.

Compound $(B)$ is

$C_6H_6$ $\xrightarrow[AlCl_3]{(CH_3)_2CHCOCl}$ $\xrightarrow[\text{reduction}]{\text{Clemmensen}}$ $\xrightarrow[AlCl_3]{CH_3COCl}$ $\xrightarrow[\text{Red } P + HI]{H_3O^{\oplus}} (\text{Ibuprofen})$
Ibuprofen is

The reaction sequence is:
$2-\text{hydroxycyclohexylacetone}$ $\xrightarrow{I_2/NaOH}$ $\xrightarrow{\Delta}$ $\xrightarrow{H^+}$ $\xrightarrow{\Delta} A$
$A$ is: