Hi,
There are many government colleges which provide degree in food nutrition . You can either go for btech from food technology or you can also pursue bsc in food science .
Generally admission is given on the basis of marks scored in 12 class or they conduct their own test.
Generally students opt food nutrition as a course in msc and they simply do bsc with food science .
There are good  colleges which include
Mount Caramel College, Bangalore
Women's Christian College, Chennai
Mahatma Jyoti Rao Phoole University, Jaipur
Hope it helps thank you