VNIT Nagpur - Visvesvaraya National Institute of Technology

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Yes, you can get admission for B.Tech lateral entry.

Please refer to the link provided below for details regarding eligibility and admission procedure followed to secure a seat in M.Tech in Construction Technology and Management Engineering from Visvesvaraya National Institute of Technology. Details like fees, course structure, placements, etc. are also available at this link.
Regards.
https://www.shiksha.com/engineering/course/m-tech-in-construction-technology-and-management-engineering-visvesvaraya-national-institute-of-technology-nagpur-297718

For B.Sc in VNIT, Nagpur, you have to appear for JEE Mains. Then, after it's counselling, you would be able to get the college.

Follow the link below for details:
https://www.shiksha.com/b-tech/course/b-tech-in-computer-science-and-engineering-visvesvaraya-national-institute-of-technology-Nagpur-61703.

VNIT, Nagpur does not offer a course in Aeronautical engineering. Please refer to the link provided below for a list of courses offered by this college. https://www.shiksha.com/college/visvesvaraya-national-institute-of-technology-nagpur-24399.

Admission is through JOSAA counselling based on the rank obtained in JEE Mains. Marks required to secure admission keeps changing and you should wait for cut offs to be declared if you want admission in Visvesvaraya National Institute of Technology for B.Arch. Your HSC marks are sufficient, you need to wait for cut offs to be declared by Visvesvaraya National Institute of Technology to pursue a course in B.Arch. Regards.

You should definitely go with MITS, because it is highly reputed college of Central India and have better placement record.