Concept:
The sodium nitroprusside test is used for the detection of sulphur-containing compounds.
When an organic compound containing sulphur is fused with sodium, sodium sulphide is formed.
The sodium fusion extract containing sulphide ions reacts with sodium nitroprusside to produce a characteristic violet or red-blood coloured complex.
Step 1: Identify sulphur-containing amino acids.
Among naturally occurring amino acids:
Methionine and Cysteine
contain sulphur atoms.
Step 2: Examine the given options.
Serine:
\[
HOCH_2CH(NH_2)COOH
\]
contains oxygen but no sulphur.
Leucine:
Contains only carbon, hydrogen, oxygen and nitrogen.
No sulphur is present.
Threonine:
Contains hydroxyl group but no sulphur.
Methionine:
\[
CH_3-S-CH_2-CH_2-CH(NH_2)-COOH
\]
contains sulphur.
Therefore it gives the sodium nitroprusside test.
Step 3: Conclusion.
Since methionine contains sulphur, its sodium fusion extract forms sulphide ions which react with sodium nitroprusside producing a characteristic red-blood colour.
Hence,
\[
\boxed{\text{Methionine}}
\]
is the correct answer.