Concept:
Grignard reagents react with carbonyl compounds to produce alcohols.
\[
R-MgX + HCHO \xrightarrow{H_3O^+} RCH_2OH
\]
The alcohol can be converted into an alkyl bromide using \(PBr_3\), and subsequent reduction with \(Zn/dil.~H^+\) gives the corresponding alkane.
The alkane formed must satisfy the condition that it produces only one monochloro derivative on photochemical chlorination.
Step 1: Analyze the condition regarding monochlorination.
Only those alkanes produce a single monochloro product in which all hydrogen atoms are equivalent.
Examples:
\[
CH_4,\quad C_2H_6,\quad (CH_3)_4C
\]
Among higher alkanes, neopentane
\[
(CH_3)_4C
\]
gives only one monochloro derivative because all twelve hydrogen atoms are equivalent.
Hence the alkane obtained after reduction must be
\[
\boxed{\text{Neopentane}}
\]
Step 2: Determine the alcohol required.
The corresponding alcohol is
\[
(CH_3)_3CCH_2OH
\]
(neopentyl alcohol).
Reaction sequence:
\[
(CH_3)_3CCH_2OH
\xrightarrow{PBr_3}
(CH_3)_3CCH_2Br
\]
\[
(CH_3)_3CCH_2Br
\xrightarrow{Zn/dil.H^+}
(CH_3)_3CCH_3
\]
which is neopentane.
Step 3: Find the Grignard reagent and carbonyl compound producing neopentyl alcohol.
Methanal reacts with tert-butyl magnesium bromide as:
\[
HCHO + (CH_3)_3CMgBr
\]
followed by hydrolysis gives
\[
(CH_3)_3CCH_2OH
\]
(neopentyl alcohol).
Thus
\[
A = HCHO
\]
and
\[
B = (CH_3)_3CMgBr
\]
Step 4: Verify the complete sequence.
\[
HCHO
\xrightarrow[(H_3O^+)]{(CH_3)_3CMgBr}
(CH_3)_3CCH_2OH
\]
\[
(CH_3)_3CCH_2OH
\xrightarrow{PBr_3}
(CH_3)_3CCH_2Br
\]
\[
(CH_3)_3CCH_2Br
\xrightarrow{Zn/dil.H^+}
(CH_3)_3CCH_3
\]
(neopentane)
\[
(CH_3)_3CCH_3
\xrightarrow{Cl_2/h\nu}
\text{only one monochloro derivative}
\]
Hence all conditions are satisfied.
Therefore,
\[
\boxed{A=HCHO,\qquad B=(CH_3)_3CMgBr}
\]
\[
\boxed{\text{Correct Option = (4)}}
\]