Hi! Firstly, I would recommend you to search for a decent NIT as per your rank, since they are some of the best engineering colleges in India. I'm providing you the link in which you will get all the important information regarding the previous year cutoffs or opening and closing rank of various NITs for all branches. You can check this link by comparing your score and rank.

https://www.google.com/amp/s/engineering.careers360.com/articles/nits-cutoff-for-top-btech-branches/amp

Now, as for the private college in Hyderabad, I have attached the following link as a reference for all the top private colleges in Hydrabad. It contains all the neccessary information, regarding JEE Mains score required for specific branches, courses, fees, etc-

https://engineering.careers360.com/colleges/list-of-private-engineering-colleges-in-hyderabad

All the best!