Hi aspirant,
You have completed your BSc in biomedical biotechnology from private college. Yes, you can do MSc in biotechnology from JNU or other universities. You may need to satisfy some other criteria as well.
The basic eligibility criteria required for ICAR PG examination is that the Candidates must have completed their graduation in a related field from a recognised college/ institute. 10+2 education from CBSE or any other recognized board in English medium with at least any three Science subjects out of Mathematics, Physics, Chemistry, and Biology. And you meet this. So you are eligible provided you also meet the other criteria like age limit and others.
All the best.
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