Hello student cut off vary every year on various factors like level of questions in the examination total number of applicants and seats offered.

As you've not mentioned your category, considering you as a general category student it's difficult to get admission in NITs or IIITs. As in NIT or IIITs admission is based on jee main marks/rank only you class 12 marks is not considered.

Yes you can apply in Christ university if you're willing to pursue B.tech from Christ university.

ELIGIBILITY - Candidates must passed or appearing class 12 in physics chemistry and Mathematics with minimum 50 percent marks from a recognized board.

You can use Careers360 college predictor to predict college. -

Feel free to comment if you've any doubt

Good luck