Hello Atharva
Names of some of the B.Sc. Biotechnology entrance exams are
AIIMS Biotechnology Entrance Test
JNU (Jawaharlal Nehru University) Combined Biotechnology Entrance Examination
CBEEE (Combined Biotechnology Entrance Examination)
DU (University of Delhi) Biotechnology Entrance Examination.

Some of the colleges offering B.Sc. Biotechnology are listed
AIIMS, New Delhi
Fergusson College, Pune
Christ University, Bangalore
Presidency University, Kolkata
Manipal University, Karnataka
Loyola College, Chennai
Mount Camel College, Bangalore
Madrass Christian College, Chennai
Jamia Milia Islamia, New Delhi
Delhi University, Delhi