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Hi Mridul,
With the JEE score of 13901 your admission in:
1) IIT is very less likely as the cut off for ST category ranges between 1500-2000.
2) NIT is possible but only in newer and less competitive branches like NIT Goa, NIT Srinagar, NIT Sikkim etc. You may also avail home state quota if you belong to the same state where the NIT is situated.
3) You have good chances to get enrolled in a GFTI, as they have lower cutoffs. Few famous GFTI are:
ALL THE BEST!
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