sorry!! its not posiible to you to get any colleges for the rank you provided.

Yes with this rank you don't have to worry about your admissions as in general if you get a rank below 20k you could easily get admission in top NITs or other government colleges that too in core branches. The counselling process is yet to be start you need to wait  for that till than you can predict the colleges you might be getting with the help of jee main college predictor and you can also have a look on previous year cut offs of nits.
https://engineering.careers360.com/jee-main-college-predictor
https://engineering.careers360.com/articles/jee-main-cutoff-for-top-nits?amp
Good Luck!!

Sorry it look little impossible to get addmisision in govt. Teason is clear rank is too high .
Please give us your marks and state and category too.

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