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Hey,
I read your problem statement , I am providing you link and some article. this is careers360 college predictor tool and previous year cut offs. it will help you alot. However according to me you will face difficulty in finding college.. Hope that it is helpful to you. wish you all the best.
regards
https://engineering.careers360.com/jee-main-college-predictor?icn=jee-main-clgpd_landing-page&ici=prediction-section_c360-home
https://engineering.careers360.com/articles/jee-main-cutoff-for-top-nits
https://engineering.careers360.com/articles/nits-cutoff-for-top-btech-branches
https://engineering.careers360.com/articles/jee-main-cutoff-for-top-gftis
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