Identify the sequence up to compound $Q$

We are told:

• $O \xrightarrow[ ]{KMnO_4/H^+} P$
• $P \xrightarrow[\Delta]{NH_3} Q$
• $Q \xrightarrow[]{Br_2/NaOH} R$

Since heating a carboxylic acid with ammonia gives an amide, $P$ must be a carboxylic acid and $Q$ its amide.

Also, treatment of an amide with $Br_2/NaOH$ is Hofmann bromamide degradation, which converts: $RCONH_2 \longrightarrow RNH_2$ with loss of one carbon atom.

A very common oxidation is: $CH_3COOH \xrightarrow[]{NH_3,\Delta} CH_3CONH_2$ and then $CH_3CONH_2 \xrightarrow[]{Br_2/NaOH} CH_3NH_2$

So the consistent identification is: $P = CH_3COOH \quad (\text{acetic acid})$ $Q = CH_3CONH_2 \quad (\text{acetamide})$ $R = CH_3NH_2 \quad (\text{methylamine})$

Find compound $S$ from strong heating of $Q$

Strong heating of an amide like acetamide causes dehydration to give the corresponding nitrile: $CH_3CONH_2 \xrightarrow[\text{strong heat}]{} CH_3CN$

Hence, $S = CH_3CN \quad (\text{acetonitrile})$

Reaction of nitrile with ethyl 2-bromopropanoate in presence of $KOH$

Ethyl 2-bromopropanoate is: $BrCH(CH_3)COOEt$

In presence of base, acetonitrile forms the carbanion at the alpha-carbon: $CH_3CN \xrightarrow[]{KOH} ^{-}CH_2CN$

This undergoes nucleophilic substitution with ethyl 2-bromopropanoate: $^{-}CH_2CN + BrCH(CH_3)COOEt \rightarrow CH_3CH(COOEt)CH_2CN$

On acidification/hydrolysis, both functional groups are converted appropriately, and the nitrile gives a carboxylic acid. Thus: $CH_3CH(COOEt)CH_2CN \xrightarrow[]{H^+} CH_3CH(COOH)CH_2COOH$

This corresponds to an amino acid precursor route. In standard synthesis context, the product obtained corresponds to alanine after the usual conversion sequence from the nitrile-derived intermediate.

Among the given amino acids, this chain structure matches alanine.

Check options

• A: Glycine — would require no methyl substituent on the alpha-carbon; not consistent.
• B: Alanine — consistent with use of 2-bromopropanoate introducing the $CH_3$ substituent.
• C: Valine — would require an isopropyl side chain; not formed here.
• D: Serine — would require a hydroxymethyl side chain; not formed here.

Final answer

$\boxed{\text{B: Alanine}}$