You can consider below names -
Jawaharlal Nehru University - New Delhi
The placements are offered by companies such as biocon, ranbaxy. Further, 60-70% get placed in research labs as phd students and junior research fellows. The starting salary was 25K.

NIT (Warangal, Surathkal, Calicut, Trichy )
UNIVERSITY OF HYDERABAD - [UOH], HYDERABAD
NATIONAL INSTITUTE OF MANAGEMENT - [NIM], MUMBAI
PONDICHERRY UNIVERSITY, PONDICHERRY
VELLORE INSTITUTE OF TECHNOLOGY - [VIT UNIVERSITY], VELLORE etc.

Hope this helps!!!