Yes, very much possible. Read section 149 of the Companies Act, 1956.
The date of incorporation of a company may not be the date of commencement of business. A private company and a public limited company not having share capital are not required to comply with any other formalities and may commence its business activities immediately after obtaining the certificate of incorporation from the concerned Registrar of Companies. A private limited company and a public limited company not having share capital can start its business immediately on its incorporation without any restrictions. A private limited company, which has converted into public limited company, is also not required to obtain certificate of commencement of business.