Which of the following statement(s) is/are true?

Options

A. Titan yellow solution gives red colouration with a neutral solution containing `Mg^(2+)` ions
B. Solution of nitrile is decomposed by sulphamic acid.
C. `Fe^(2+)` ions give brown colour precipitate with `[Fe(CN)_(6)]^(3-)` ions solution.
D. Green precipitate of `Cr(OH)_(3)` is soluble in `Na_(2)O_(2)`

Explanation

To determine which of the statements provided are true, we will analyze each statement step-by-step.

### Step 1: Analyze Statement A
**Statement A:** Titan yellow solution gives red coloration with a neutral solution containing Mg²⁺ ions.

- **Analysis:** Titan yellow is a pH indicator that typically shows a red color in alkaline solutions when it reacts with Mg²⁺ ions. In a neutral solution, it does not exhibit this red coloration. Therefore, this statement is **incorrect**.

### Step 2: Analyze Statement B
**Statement B:** The solution of nitrile is decomposed by sulphamic acid.

- **Analysis:** Sulphamic acid (HO, SO₂, NH₂) can react with nitrile (R-C≡N) to produce nitrogen gas (N₂), water (H₂O), and sulfuric acid (H₂SO₄). The reaction can be represented as:

\[ R-C≡N + HO, SO₂, NH₂ \rightarrow N₂ + H₂O + H₂SO₄ \]

This shows that nitrile does decompose in the presence of sulphamic acid. Thus, this statement is **correct**.

### Step 3: Analyze Statement C
**Statement C:** Fe²⁺ ion gives a brown color precipitate with Fe(CN)₆³⁻ ion solution.

- **Analysis:** The complex Fe(CN)₆³⁻ typically reacts with Fe³⁺ ions to form a brown precipitate. Fe²⁺ does not form a brown precipitate with this complex. Therefore, this statement is **incorrect**.

### Step 4: Analyze Statement D
**Statement D:** The green precipitate of Cr(OH)₃ is soluble in Na₂O₂.

- **Analysis:** Cr(OH)₃, which is a green precipitate, reacts with sodium peroxide (Na₂O₂) to form chromate ions (CrO₄²⁻), which are yellow in color. The reaction can be summarized as:

\[ Cr(OH)₃ + O₂²⁻ \rightarrow CrO₄²⁻ + H₂O \]

Since CrO₄²⁻ is soluble, this statement is **correct**.

### Conclusion
Based on the analysis:
- Statement A: Incorrect
- Statement B: Correct
- Statement C: Incorrect
- Statement D: Correct

Thus, the true statements are B and D.

### Final Answer
The correct answers are **B and D**.

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