Architecture

You can look for NIT-Warangal and Calicut. Also, the chances of getting into JJ College are also there. DY Patil is also a good option for you.

I think, NATA score is needed for the same.

No, you can't. They offer admission through NATA.

NATA score is considered.

It's around 1.5-2 lacs for a year.

No, you have to crack the entrance exam conducted by Anna University.

The selection is based on your JEE Mains Paper-2 Rank. Last year (2017) Closing Rank for: Chandigarh Candidates : 7910
Non-Chandigarh Candidates: 2362
So if you want to get admission you need to be under the cutoff rank of JEE paper 2 then only you will have chances to get into Chandigarh college of architecture.

Registration for Architecture Aptitude Test commences after the announcement of IIT-JEE Advanced results. Eligibility Criteria for AAT Only the applicants who successfully qualified JEE Advanced can appear for AAT to get admission to B.Arch. Hence you are not allowed for AAT examination because you did not write JEE Advanced.

You have scored well in JEE and you have scored a great rank and yes, you can get a seat in NITs.

To apply for scholarship under Post-matric Scholarship Scheme for SCs/OBCs students, please visit:
http://www.punjabscholarships.gov.into apply for scholarship under Scholarship Scheme for Minorities students, and
Central Sector Scholarship Scheme for College and University students, please visit:
https://www.scholarships.gov.in/To apply for AICTEs scholarship for J & K students, please visit;
http://www.aicte-jk-scholarship-gov.in/.