There are no engineering colleges in India (as per the data) which offers admission entirely based on the 10+2 results. Thus in order to take admission in BTech there are no options for you but you have to qualify entrance. You may get preferences in admission during admission in colleges, but you will not get admission in the colleges without any entrances.

Some of the best colleges in UP for BTech are:

MNNIT Allahabad - Motilal Nehru National Institute of Technology Allahabad Prayagraj

HBTU Kanpur - Harcourt Butler Technical University

Integral University, Lucknow

IIT BHU - Indian Institute of Technology Banaras Hindu University

IIT Kanpur - Indian Institute of Technology

For more colleges you may visit the link provided below:

https://engineering.careers360.com/colleges/list-of-engineering-colleges-in-uttar-pradesh

I hope this answer helps. All the very best for your future endeavors!