Is entrance exam compulsory for the admission in BBA?

Entrance exam for BBA is depend upon the college where you pursued. If you are willing to take admission in Ness Wadia, there is no entrance exam for BBA.

It isn't mandatory. Many BBA colleges in India give admission based on student's past academic records. Very few colleges/universities take entrance exam and interview before admission process. But nothing is there to worry about. These entrance exams are really very easy to crack unlike CAT exam.