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.
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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.