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Hi Shahid,
There are quite many government institutions bin Uttar Pradesh for engineering. There are those who admit through JEE mains and advanced or UPSEE. The top ones are surely the IITs which are in Kanpur and Varanasi. There are two IIITs in Allahabad and Lucknow and Motilal Nehru NIT in Allahabad which are really good. There are more good options to go for. You can check this link-
https://engineering.careers360.com/colleges/ranking/top-engineering-colleges-in-uttar-pradesh
All the best!
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