Hello Anannya, 

Calcutta University have undertaken several colleges who offers multiple types of courses and as your interest is in BBA, then yes they also provide the degree of BBA.

The colleges under Calcutta University which do so are Ashutosh, St. Xaviers and some more. 

You can apply for BBA course out there and for more information, you can also refer to the official website of Calcutta University.