Which of the following cation does not give red colour precipitate/solution with dimethylglyoxime `(DMG)` in alkaline solution?

Options

A. `Zn^(+2)`
B. `Ni^(+2)`
C. `Fe^(2+)`
D. both (A) and ( C)

Explanation

To determine which cation does not give a red color precipitate or solution with dimethylglyoxime (DMG) in alkaline solution, we will analyze the behavior of the given cations when they react with DMG.

### Step-by-Step Solution:

1. **Identify the Cations**: The cations provided in the options are Zinc (Zn²⁺), Nickel (Ni²⁺), Iron (Fe²⁺), and both A (Zinc) and C (Iron).

2. **Understand the Reaction with DMG**: Dimethylglyoxime (DMG) is a bidentate ligand that forms colored complexes with certain metal ions in alkaline solutions. The formation of these complexes can be tested to identify which metal ions react to produce a red color.

3. **Analyze Iron (Fe²⁺)**:
- When Fe²⁺ reacts with DMG in an alkaline medium, it forms a complex.
- The complex formed is red in color.
- Therefore, Fe²⁺ gives a red color precipitate with DMG.

4. **Analyze Nickel (Ni²⁺)**:
- Nickel also reacts with DMG in an alkaline solution.
- It forms a red-colored complex as well.
- Hence, Ni²⁺ also gives a red color precipitate with DMG.

5. **Analyze Zinc (Zn²⁺)**:
- Zinc, when treated with DMG in an alkaline medium, does not form a red-colored complex.
- Instead, it typically forms a colorless or white precipitate.
- Therefore, Zn²⁺ does not give a red color precipitate with DMG.

6. **Conclusion**:
- From the analysis, we can conclude that the cation that does not give a red color precipitate with DMG in alkaline solution is Zinc (Zn²⁺).

### Final Answer:
The cation that does not give a red color precipitate with dimethylglyoxime in alkaline solution is **Zinc (Zn²⁺)**.