What are the forms in which business can be conducted by a foreign company in India?

A foreign company planning to set up business operations in India has the following options: 

As an incorporated entity by incorporating a company under the Companies Act, 1956 through: [1] Joint Ventures; or [2] Wholly Owned Subsidiaries 
As an office of a foreign entity through  Liaison Office / Representative Office,  Project Office,  Branch Office 
Such offices can undertake activities permitted under the Foreign Exchange Management (Establishment in India of Branch Office or other place of business) Regulations, 2000.