Since you have not mentioned the name of any NIT or your category or the field *-u are interested. So, I will be telling cutoff range [GATE] for NIT Trichy, OPEN, and few known fields
FOR CSE: 807-643
FOR CHEMICAL ENGINEERING: 712-466
FOR COMMUNICATION SYSTEM: 766-681
The gateway for admission into NITs is JEE main. Different varieties have different cutoffs specific to their stream and ranking. The top in NIT such as Rourkela, tiruchirappalli, Warangal, have the average cutoff of above 98 percentile in general.
There is also state quota reservation for local candidates, which have a lower cutoff than other state students, which is provided to the domicile holders.
Hope it helps!!