Delhi University (It offers BMS)

NMIMS University, Mumbai

IIM-Indore (Dual degree program)

IP university (Delhi)

Symbiosis International University (Pune )

Christ university(Bangalore )

NOTE: For Delhi University and NMIMS, you require mathematics as an eligibility criterion.No College offers 100 % placement. It will depend upon your capability and potential. You can get through the colleges by clearing the following entrance :

Entrance Exams

Joint Admission Test (JAT for Delhi University)

GGSIPU CET BBA(Guru Gobind Singh Indraprastha University, Delhi)

IPMAT (IIM Indore Integrated Program In Management Aptitude Test)

AIMA-UGAT:- All India Management Association BBA Entrance Examination

Symbiosis Entrance Test (SET)

P.s - IIM Indore, IPM
Its a 5 year integrated program in management, I didt include it in the above four as its completely a different course for a career. You freeze your next 5 years and dont get a PGDM which an IIM gives after getting admit into one via CAT.
Be ready for a fierce competitive test for IPM an an equally grilling interview, can say it from my personal experience.