A red colouration or precipitate is not obtained when:

Options

A. `Fe^(3+)` reacts with potassium thiocyanate
B. `Fe^(2+)` reacts with dimethylglyoxime.
C. `Hg^(2+)` reacts with potassium iodide.
D. None

Explanation

To solve the question "A red colouration or precipitate is not obtained when:", we need to analyze the given options and determine which reaction does not yield a red coloration or precipitate.

### Step-by-Step Solution:

1. **Identify the Reactions**:
We have four reactions to consider. Let's analyze each one to see if it produces a red precipitate or coloration.

2. **Reaction 1**:
- **Fe³⁺ + KSCN**:
- When iron (III) ions (Fe³⁺) react with potassium thiocyanate (KSCN), they form a complex ion [Fe(SCN)]²⁺, which is known to produce a red coloration.
- **Conclusion**: This reaction produces a red color.

3. **Reaction 2**:
- **Fe²⁺ + DMG**:
- Iron (II) ions (Fe²⁺) react with dimethylglyoxime (DMG) to form a red precipitate of the complex [Fe(DMG)₂].
- **Conclusion**: This reaction also produces a red precipitate.

4. **Reaction 3**:
- **Hg²⁺ + KI**:
- Mercury (II) ions (Hg²⁺) react with potassium iodide (KI) to form mercury(I) iodide (Hg₂I₂), which appears as a red precipitate.
- **Conclusion**: This reaction produces a red precipitate as well.

5. **Reaction 4**:
- **Identify the missing option**:
- Since the first three reactions produce red colorations or precipitates, we need to identify the fourth option that does not yield a red coloration.
- If no specific fourth reaction is provided, we can conclude that the answer is "none of these" as all the mentioned reactions yield red colorations or precipitates.

### Final Answer:
The correct answer is **Option D: None of these**, as all the reactions listed produce a red coloration or precipitate.