Does NMIMS has any integrated management course for students like after BBA, students can directly pursue MBA without any entrance exam?

NMIMS does offer an integrated MBA program, but that is only for the family business specialization. Kindly go through the below link for more details. http://www.nmims.edu/admissions/

We can modify your doubts. NMIMS have integrated course. You will get preference, if you are doing Bachelors from that particular college, but at the same time you have to appear for NMAT exam.