The compound (X) with M.F. `C_(4)H_(11)N` on treatment with `HNO_(2)` gives a tertiary alcohol with M.F. `C_(4)H_(10)O`. The compound (X) will give

Options

A. Carbylamine reaction
B. Hofmann mustard oil reaction
C. Diazonium salt as intermediate with `HNO_(2)`
D. Gives 2-methyl-2-nitropropane on oxidation with `KMnO_(4)`

Explanation

To solve the question, we need to analyze the information given about the compound (X) with the molecular formula \( C_4H_{11}N \).

### Step-by-Step Solution:

1. **Identify the Type of Amine**:
- The molecular formula \( C_4H_{11}N \) indicates that the compound (X) is an amine. Given that it reacts with \( HNO_2 \) to produce a tertiary alcohol, we can deduce that (X) is a primary amine. This is because primary amines react with nitrous acid to form alcohols.

**Hint**: Recall that primary amines yield alcohols upon reaction with nitrous acid.

2. **Determine the Structure of Compound (X)**:
- A primary amine with the formula \( C_4H_{11}N \) can be represented as \( R-NH_2 \). The simplest structure that fits this formula is \( CH_3-CH_2-CH_2-NH_2 \) (butylamine) or \( (CH_3)_2CH-NH_2 \) (isobutylamine). Both are valid structures for primary amines.

**Hint**: Consider the structural possibilities for a primary amine with four carbons.

3. **Reaction with \( HNO_2 \)**:
- When a primary amine reacts with nitrous acid (\( HNO_2 \)), it forms a diazonium salt as an intermediate, which then decomposes to form an alcohol. The resulting alcohol has the formula \( C_4H_{10}O \), which is consistent with a tertiary alcohol.

**Hint**: Remember that primary amines form diazonium salts which can decompose to give alcohols.

4. **Identify the Product**:
- The product formed is a tertiary alcohol with the molecular formula \( C_4H_{10}O \). This suggests that the alcohol has a branched structure, likely \( (CH_3)_3C-OH \) (tert-butanol), which is consistent with the reaction of a primary amine.

**Hint**: Think about how the structure of the alcohol relates to the original amine structure.

5. **Conclusion**:
- Therefore, the compound (X) is a primary amine that upon treatment with \( HNO_2 \) gives a tertiary alcohol. The possible reactions that (X) can undergo include the formation of diazonium salts and the mustard oil reaction.

**Hint**: Primary amines can undergo multiple reactions, including forming diazonium salts and participating in mustard oil reactions.

### Final Answer:
The compound (X) will give:
1. Diazonium salt (as an intermediate).
2. Tertiary alcohol upon reaction with \( HNO_2 \).
3. It will also respond to the mustard oil reaction.