During the qualitative analysis of salt with cation $$y^{2+}$$, addition of a reagent (X) to alkaline solution of the salt gives a bright red precipitate. The reagent (X) and the cation ($$y^{2+}$$) present respectively are :

We need to identify the reagent (X) and cation ($$y^{2+}$$) that gives a bright red precipitate in alkaline solution.

Key observation: A reagent added to an alkaline solution of a salt containing $$y^{2+}$$ gives a bright red precipitate.

Analysis of options:

Option A: Dimethylglyoxime (DMG) and Ni²⁺

Dimethylglyoxime reacts with $$Ni^{2+}$$ ions in an alkaline (ammoniacal) solution to form a bright red (rosy red) precipitate of nickel dimethylglyoximate:

$$Ni^{2+} + 2 \text{DMG} \xrightarrow{NH_4OH} \text{Ni(DMG)}_2 \downarrow \text{ (bright red)}$$

This is a classic confirmatory test for $$Ni^{2+}$$ ions in qualitative analysis.

Option B: Dimethylglyoxime and Co²⁺

DMG does not give a bright red precipitate with $$Co^{2+}$$. Cobalt with DMG gives a different colored complex.

Option C: Nessler's reagent and Hg²⁺

Nessler's reagent ($$K_2[HgI_4]$$) is used to detect $$NH_4^+$$ ions (gives brown precipitate), not for $$Hg^{2+}$$.

Option D: Nessler's reagent and Ni²⁺

Nessler's reagent is not used for $$Ni^{2+}$$ detection.

The correct answer is Option A: Dimethylglyoxime and Ni$$^{2+}$$.