Science

For M.sc Mathematics the eligibility criteria at Lovely professional university is Pass with 55% aggregate marks in Bachelor's degree (any discipline) (with Mathematics as a subject) or B.Tech. or B.E. or B.Sc. (Engineering) or equivalent.
This is a versatile two year (four semesters) programme that

The eligibility criteria for KVPY 2020 (a) Stream SA: Students enrolled in the XI Standard (Science Subjects) during the academic year 2020-21 and having secured a minimum of 75% (65% for SC/ST/PWD) marks in aggregate in MATHEMATICS and Science subjects (Physics/Chemistry/Biology) in the X Standard

As per the year 2019-20 placement statistics of IIT-B for 2 year M.Sc in biotechnology. Total 13 students has been participated in placement. Out of which 7 students get placed with 53.85% of students participated in placement.

You have not written about the rank you obtained in NEET. However, your expected rank is between 246358-262168. Based on the rank, you can get the following.
1. Dr. D. Y. Patil Medical College, Hospital and Research, Pune
2. D. Y. Patil Medical College, Kolhapur
3. Padmashree Dr. D. Y. Patil Vidyapeet