A reagent which gives brilliant red precipitate with Nickel ions in basic medium is

Step 1: Analyze the Options

We need a reagent that produces a "brilliant red precipitate" with $\ce{Ni^{2+}}$ ions under basic conditions (typically an ammonium hydroxide medium).

• Sodium nitroprusside: Used for sulphide ($\ce{S^{2-}}$) detection, giving a purple color.
• Neutral $\ce{FeCl3}$: Used to detect phenols and certain ions like acetate, giving characteristic colored solutions, not red precipitates with Nickel.
• Meta-dinitrobenzene: Forms colored complexes via Janovsky reaction, mostly for active methylene compounds.
• Dimethyl glyoxime (DMG): An organic precipitating agent well-known for forming a distinct brilliant red (rosy red) precipitate with Nickel(II) ions.

Step 2: Reaction with DMG

When $\ce{Ni^{2+}}$ ions react with Dimethylglyoxime (DMG) in the presence of ammonium hydroxide (mildly basic medium), a square planar, bright red complex called Nickel dimethylglyoximate is formed.

$\ce{Ni^{2+} + 2DMG -> [Ni(DMG)2] v + 2H+}$ (The reaction goes to completion in a mild base that neutralizes the $\ce{H+}$ produced).

Step 3: Conclusion

The reagent is unequivocally dimethyl glyoxime.

Key Points to Remember:

• Nickel(II) gives a rosy red/brilliant red precipitate with DMG in an ammoniacal medium.
• The complex $\ce{[Ni(DMG)2]}$ is square planar, diamagnetic, and is stabilized by strong intramolecular hydrogen bonds.
• Sodium nitroprusside gives a violet/purple color with $\ce{S^{2-}}$.