Yes, After completing 2nd PUC with Science you can apply for BBA programme. Generally, the top BBA colleges in India are affiliated to universities. The Top BBA Colleges in India are mainly affiliated by the following universities:

University of Delhi

Guru Gobind Singh Indraprastha University, Delhi

University of Mumbai

Symbiosis International University, Pune

NMIMS University, Mumbai

Bharati Vidyapeeth Deemed University, Pune

Christ University, Bangalore

Gitam University, Vishakhapatnam

Good Luck!