India

To get the best government college in any year, 625+ marks is needed as per standard. And mostly, 550 is closing cut off for AIQ but chances of getting state government quota seat for states like Andhra Pradesh, Kerala for 500 is not possible. So, aim for 550+. You can.
Good luck.

You can get the list of the best B.Tech college with full information and review:
https://www.shiksha.com/b-tech/ranking/top-engineering-colleges-in-Telangana/44-2-413-0-0.

You can get the list of top colleges in Maharashtra for BBA by the given:
https://www.shiksha.com/bba/ranking/top-bba-colleges-in-Maharashtra/93-2-114-0-0.

Dear!
You could have much better options then Anna University in south India. If the private college is technical only options you are left with then you may consider VIT Vellore or SRM Chennai for B.Tech. Anna is not up to the mark. It's ranking is low and placement index is also not high as such.
Hope this helps.
Good Luck.

No, they don't.
CAT, XAT, MAT are the accepted entrance tests. Kindly apply with any of the mentioned test scores.

You can use Shiksha college predictor to know about your chances.
Link: https://www.shiksha.com/b-tech/resources/ts-eamcet-college-predictor.

Mahatma Gandhi Chitrakoot Gramodaya Vishwavidyala, Swami Vivekanad University-Sagar, AKS University are some of the institutes offering B.Tech in Food Technology. Check the below link for more information about these institutes- https://www.shiksha.com/b-tech/colleges/b-tech-in-food-technology-colleges-madhya-pradesh.