JEE

Kindly elaborate your question.

The colleges are LPU, Amity, Manipal (in top 10 for architecture), SRM, BMS College of Engineering, R V College of Architecture, Lingaya's University and Modi University.

Yes, you can surely get CSE but the colleges may not be good. I would suggest you to apply in SRM or VIT by giving their exams.

You'll only get private colleges with this rank.

You have to pass the minimum criteria required to get admission through JEE Mains.

You might have a chance if you have any reservation criteria else give it a try. You have very great chance to get into this institute with this rank. Attend the counselling and choose your options appropriately. Try Shiksha college predictor for better analysis.

No, you can't get this college by other states quota. Because it's cut off is very high for others state students.

I am enlisting top colleges with their fee structure:
Centre For Environmental Planning & TechnologyAhmedabad-1,61,000
Lovely Professional University - 19500
Jadavpur UniversityKolkata-2,730
School of Planning and Architecture Delhi-46,300
NIMS UniversityJaipur-1,11,000
Sir J. College Of ArchitectureMumbai-17,800
Indian Institute of TechnologyKharagpur-74,000
National Institute of TechnologyThiruchirapalli-39,400
Jamia Millia IslamiaNew Delhi-64,500
Manipal UniversityManipal-3,04,000

I am enlisting top colleges with their fee structure:
Centre For Environmental Planning & TechnologyAhmedabad-1,61,000
Lovely Professional University - 19500
Jadavpur UniversityKolkata-2,730
School of Planning & Architecture Delhi-46,300
NIMS UniversityJaipur-1,11,000
Sir J. College Of ArchitectureMumbai-17,800
Indian Institute of TechnologyKharagpur-74,000
National Institute of TechnologyThiruchirapalli-39,400
Jamia Millia Islamia New Delhi-64,500
Manipal UniversityManipal-3,04,000

Go to Kotak or Indore otherwise Delhi will be good option for preparation of IIT-JEE. These cities have good atmosphere for study.