Introduction:
In order to understand the correct answer, it is important to have a clear understanding of the process of commencing business for a private limited company. The process involves obtaining certain legal documents and fulfilling various legal requirements.

Certificate of Incorporation:
The certificate of incorporation is a legal document issued by the Registrar of Companies, which signifies the creation of a new company. It confirms that the company has been registered under the Companies Act and has a separate legal existence. This certificate includes important details such as the company name, registered office address, and the date of incorporation.

Certificate to Commence Business:
After obtaining the certificate of incorporation, a private limited company needs to obtain a separate certificate to commence business. This requirement was introduced by the Companies (Amendment) Act, 2015, in order to ensure that companies do not start their operations immediately after incorporation without adequate capital and proper compliance.

The certificate to commence business is issued by the Registrar of Companies only when the following conditions are met:

1. Subscription of shares: The company must have received a minimum subscription of shares as stated in its prospectus. This ensures that the company has sufficient capital to carry out its business activities.

2. Declaration by directors: The directors of the company must file a declaration stating that the minimum subscription has been received and the company has complied with all the requirements of the Companies Act.

3. Payment of application and allotment money: The application and allotment money for the shares subscribed by the shareholders must be deposited in a separate bank account.

Correct Answer:
The correct answer is option 'B' - After obtaining the certificate of incorporation. This is because a private limited company can commence business operations only after obtaining the certificate of incorporation. The certificate to commence business is not a mandatory requirement for private limited companies.

Conclusion:
In conclusion, a private limited company can commence business after obtaining the certificate of incorporation. The certificate to commence business is an additional requirement that may be applicable depending on the circumstances of the company. It is important for companies to fulfill all legal requirements and obtain the necessary certificates before starting their operations.