At a general category rank of 60k, it's going to be difficult for you to get into a good NIT, IIIT or GFTI. You only have slight chances of getting a good college only in the spot rounds conducted by CSAB only when there are vacancies of seats in the college.
As of now, you have not mentioned your home state, therefore I would not be able to predict the best college you can get.
To know about the colleges which you can get at this rank, follow the link below:
Https://engineering.careers360.com/jee-main-college-predictor
Hope this helps!

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