Hyderabad

Colleges for B.Sc in nutrition and dietetics-
VLCC Institute of Beauty and Nutrition, Telangana, Hyderabad
VLCC Institute of Beauty and Nutrition, Bangalore
Mount Carmel College, Bangalore
Medvarsity, Bangalore
Colleges for B.Sc in physical education-
Mount Carmel College, Bangalore
Jain University, Bangalore.

I will suggest you that IMT Hyderabad is better than Nirma in terms of placement, faculty guidelines, infrastructure, etc.

If you are considering joining college without writing any exam. Than either you are looking forward to back door entry or low grade college because than only your wish will get fulfilled. Its better to give some entrance exam you can consider giving GMAT apply to some good colleges. Take your decision wisely its about your career.
All the best!

Yes, but you have to at least 70 percent to get this college.

Check this link for B.Sc courses that are available in Osmania University:
https://www.shiksha.com/university/ou-osmania-university-hyderabad-25100/courses/bsc-bc.

BIMM, Pune is better in terms of ROI and here almost 300+ companies visit almost all the sectors. The highest package this year is 14 LPA. IMT is a brand but IMT Ghaziabad is in Hyderabad with an average package of 8 LPA and minimum fees of 12 lakhs. The overall fees of BIMM is approximately 9 LPA. If you are getting an average package of 6.75 LPA then it is good.