The amine A `(C_(4)H_(11)N)` reacts with benzene sulphonyl chloride gives a product which is insoluble in aqueous NaOH then the number of alkyl group directly attached to nitrogen atom will be.

Answer

To solve the problem, we need to analyze the given information about the amine A (C₄H₁₁N) and its reaction with benzene sulphonyl chloride. We will determine the number of alkyl groups directly attached to the nitrogen atom.

### Step-by-Step Solution:

1. **Identify the Structure of Amine A:**
The molecular formula of amine A is C₄H₁₁N. We need to determine the possible structures for this amine. The presence of nitrogen suggests that it can be a primary, secondary, or tertiary amine.

2. **Calculate the Degree of Unsaturation:**
The degree of unsaturation can be calculated using the formula:
\[ \text{Degree of Unsaturation} = \frac{(C + N - H + 1)}{2} \]
Here, C = 4, H = 11, and N = 1.
\[ \text{Degree of Unsaturation} = \frac{(4 + 1 - 11 + 1)}{2} = \frac{-5}{2} = 0 \]
A degree of unsaturation of 0 indicates that there are no rings or double bonds in the structure.

3. **Determine the Type of Amine:**
Since the degree of unsaturation is 0, amine A must be a saturated compound. Given that it reacts with benzene sulphonyl chloride and forms a product that is insoluble in aqueous NaOH, we can deduce that amine A is likely a **secondary amine**. This is because primary amines typically form soluble sulphonamides in NaOH.

4. **Analyze the Reaction with Benzene Sulphonyl Chloride:**
The reaction of amines with benzene sulphonyl chloride results in the formation of sulphonamides. For a secondary amine (R₂NH), the reaction can be represented as:
\[ R_2NH + ArSO_2Cl \rightarrow R_2N-SO_2Ar + HCl \]
The product formed from a secondary amine will have two alkyl groups (R) attached to the nitrogen atom.

5. **Conclusion:**
Since we have established that amine A is a secondary amine, the number of alkyl groups directly attached to the nitrogen atom is **2**.

### Final Answer:
The number of alkyl groups directly attached to the nitrogen atom in amine A is **2**.