IIT Kharagpur - Indian Institute of Technology

The admission is given on the basis of only JEE Mains and JEE Advance score (rank).

You may have a chance of getting NIT, but you can use Shiksha college predictor tool for finding colleges:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor?utm_source=cconnect&utm_medium=CR_JEECP&utm_campaign=5836167

As ECE is one of the most sought after branch in NIT Trichy, 250+ would be a safe score as only JEE score is considered for the admissions now.

Every year the cutoff and rank criteria changes as per the no. of participants, difficulty level of questions and so many other factors which college does not reveal. Still as per the previous years cutoff criteria, we can assume what can be this year's cutoff criteria. Because it's generally near to it. Here are the previous years opening and closing ranks of ECE students. Andhra Pradesh students 3807 - 3982
Home State students 1541- 4950
Other State students 2405 -3778.

Yes, but less in number (e.g.-Central University of Jharkhand, Ranchi). Generally, nanotechnology is preferred in under-graduation or post-graduation.

Hello,
For JEE Main Paper 2, around 2 lakhs candidates appear in the Exam for seeking career in the Architecture field. Last year the JEE Main Paper 2 Cutoff was as follows
General -81 Marks
OBC -49 Marks
SC-32 Marks
ST-27 Marks
Check out the JEE Advanced Counseling from here
https://scoop.eduncle.com/jee-advanced-counselling-procedure
You can also make career in the Architecture by scoring good score in JEE Main Paper 2 as many private and govt. colleges provides B.Arch courses with good placements.