**Explanation:**

In a partnership firm, the number of partners is governed by the Partnership Act, 1932. According to Section 11 of the Partnership Act, a partnership firm having banking business becomes an illegal association when the number of partners exceeds ten.

**Reasoning:**

1. **Partnership Act, 1932:** The Partnership Act, 1932 is the governing law for partnership firms in India. It provides rules and regulations regarding the formation, operation, and dissolution of partnership firms.

2. **Definition of Partnership:** According to Section 4 of the Partnership Act, a partnership is defined as the relation between persons who have agreed to share the profits of a business carried on by all or any of them acting for all.

3. **Formation of Partnership:** A partnership can be formed with a minimum of two partners and a maximum of twenty partners in the case of a general partnership. In the case of a banking business, the maximum number of partners allowed is ten.

4. **Banking Business:** Banking business refers to the business of accepting deposits of money, lending money, and providing other financial services like issuing credit cards, loans, etc.

5. **Illegal Association:** If the number of partners in a partnership firm exceeds the maximum limit allowed by law, the partnership becomes an illegal association.

6. **Consequences:** When a partnership firm becomes an illegal association, it loses its legal status and is not recognized by law. It cannot enforce its rights, and its contracts become void.

7. **Option A - Ten:** According to the Partnership Act, a partnership firm with banking business becomes an illegal association when the number of partners exceeds ten. Therefore, option A is the correct answer.

**Summary:**

A partnership firm having banking business becomes an illegal association when the number of partners in the firm exceeds ten. This is in accordance with the provisions of the Partnership Act, 1932. It is important for partnership firms to comply with the maximum limit of partners allowed by law to maintain their legal status and enforce their rights.

Maximum number of partners for a banking business is 10.. Hence when Partners exceeds 10, it becomes an illegal association.. The new Companies Act 2013 has prescribed the maximum number of members in case of a partnership firm should not be more than 100 in case of partnerships. As per the previous Companies Act 1956, the maximum limit in case of partnerships was 10 and 20 for banking business and other businesses respectively.