Identify the characteristic test mentioned

The question says:

• the salt contains a cation $Y^{2+}$
• on adding a reagent $X$ to the alkaline solution of the salt, a bright red precipitate is obtained.

We need to identify both $X$ and $Y^{2+}$.

Recall important qualitative analysis tests

(a) Dimethylglyoxime test

Dimethylglyoxime (DMG) is a confirmatory reagent for $Ni^{2+}$.

In ammoniacal/alkaline medium, $Ni^{2+}$ gives a bright red (rose-red) precipitate of nickel dimethylglyoximate: $Ni^{2+} + 2\,DMG \rightarrow Ni(DMG)_2 \downarrow$

This is a very well-known confirmatory test for nickel.

(b) Nessler's reagent

Nessler's reagent is mainly used for detecting ammonia or $NH_4^+$, giving a brown coloration/precipitate. It is not the reagent for giving a bright red precipitate with $Ni^{2+}$ or $Hg^{2+}$.

Check each option

Option A: Dimethylglyoxime and $Ni^{2+}$

• Correct reagent for nickel confirmation.
• Gives bright red precipitate in alkaline/ammoniacal medium.
• Hence, correct.

Option B: Dimethylglyoxime and $Co^{2+}$

• DMG is not the standard confirmatory reagent for $Co^{2+}$ producing bright red precipitate.
• Hence, incorrect.

Option C: Nessler's reagent and $Hg^{2+}$

• Nessler's reagent is not used to identify $Hg^{2+}$ by bright red precipitate.
• Hence, incorrect.

Option D: Nessler's reagent and $Ni^{2+}$

• Nessler's reagent is not the confirmatory test for $Ni^{2+}$.
• Hence, incorrect.

Conclusion

The reagent is dimethylglyoxime and the cation is $Ni^{2+}$.

Therefore, the correct option is: $\boxed{A}$

Comparison with stored correct answer

Stored correct answer = A

My derived answer = A

So, they agree.