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Hello aspirant,
Congratulations for getting good rank in JEE mains 2020. As per your rank sorry to say but you have no any chances of getting free seat in IIIT or in any state institution too. According to your rank and last some years cut ffs your chances of getting admission into any good IIIT are also very low. You should go through the last years cut offs for IIITs which will clear your all doubts regarding admission chances. The link for it is provided below.
https://engineering.careers360.com/articles/jee-main-cutoff-for-top-iiits
Also I would like to suggest you to go through our college predictor tool which will be helpful for you in finding and predicting your chances in various institutions according to your rank and preferences. The link for college predictor is provided below.
https://engineering.careers360.com/jee-main-college-predictor?icn=QnA&ici=qna_answer
Best of luck.
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