Osmania University College for Women

Yes, you can go for M.Sc in nutrition and dietetics.
You must have studied Chemistry as an optional subject at graduation level any one of the subjects mentioned at graduation level- Botany/
Zoology/Genetics/Microbiology, Biochemistry and Biotechnology
Minimum graduation marks is 40%, to be eligible. The admission is through counselling, based on the marks obtained in Osmania University Common Entrance Test (OUCET). To have a look at the exam related detailed information, please click this link-
https://www.shiksha.com/university/osmania-university/oucet-exam

For this, the candidate must have studied chemistry as one of the subjects in graduation. Also, any one of the following subjects should be a part of graduation course Botany/ Zoology/ Genetics/ Microbiology, Biochemistry and Biotechnology.
For further information, please click on the following link:
https://www.shiksha.com/science/course/m-sc-in-nutrition-and-dietetics-osmania-university-college-for-women-kachiguda-hyderabad-287101

The eligibility for M.Sc. in Nutrition and Dietetics is that the candidate must have scored minimum 40% in graduation and must have studied Chemistry as an optional subject at graduation level and
Candidate must have studied any one of the subjects mentioned at graduation level:Botany/
Zoology/Genetics/Microbiology, Biochemistry and Biotechnology.
So in case if you had Chemistry and one of Botany/ Zoology/Genetics/Microbiology, Biochemistry and Biotechnology subjects you can apply for the course.
The admission is through counselling based on the marks obtained in Osmania University Common Entrance Test(OUCET)

The exam is likely to be held in June, however, there is no final confirmation on the same. For more information, please click the link below:
https://www.shiksha.com/university/osmania-university/oucet-exam-dates?q=OUCET&rf=searchwidget&landing=ep

I am not sure, but may be in the month of June, July.

Yes, there are good scope of job in the field of M.Sc in nutrition and dietetics. You can work as sport nutritionist or clinical dietician as per your interest.

Yes, you are eligible, if you have bachelor's degree with 50% aggregate and mathematics in 10+2 and graduation is compulsory. There are many good colleges offering M.Sc in Hyderabad.
All the best.

The dates for OUCET 2019 exam dates are yet to be announced.
Please stay informed about the upcoming dates from the link below.
https://www.shiksha.com/university/osmania-university/oucet-exam-dates?q=OUCET&rf=searchwidget&landing=ep