Genetics

No. JEE is not compulsory for admission into SRM. You need to write SRMJEE to be eligible for admission.

Yes, you are correct. The total intake in Masters Degree in Human Genetics at Gujarat University is 10 only.

Yes, you can get admission there.
The eligibility criteria to pursue M.Sc. (Agriculture) in Genetics & Plant Breeding is a Bachelors degree in Agriculture with second division and at least 50% marks from a recognised college or university. The duration of M.Sc. Genetics & Plant Breeding is about 2 years and its syllabus is divided into four semesters.

You are eligible to apply for M.Sc. In Nutrition.

Yes, you can choose and your eligible. In some private colleges and private universities directly you can get management seat by paying tuition fee. And coming to government universities, you have to write PGCET entrance exam for M.Sc. Human genetics. If you get good score you get best universities in state wide.