Step 1: Reaction (i).
Calcium acetate on dry distillation gives acetone:
\[
(CH_3CO)_2Ca \xrightarrow{\Delta} CH_3COCH_3
\]
So:
\[
A = CH_3COCH_3
\]
Step 2: Reaction (ii).
Acetic acid reduced with \(HI/Red\,P\) gives ethane:
\[
CH_3COOH \xrightarrow{HI,\;Red\,P} C_2H_6
\]
So:
\[
B = C_2H_6
\]
Step 3: Reaction (iii).
Two moles of acetic acid with \(P_4O_{10}\) gives acetic anhydride:
\[
2CH_3COOH \xrightarrow{P_4O_{10}} (CH_3CO)_2O
\]
So:
\[
C = (CH_3CO)_2O
\]
Final Answer:
\[
\boxed{A=CH_3COCH_3,\; B=C_2H_6,\; C=(CH_3CO)_2O}
\]