Hello

IITs are one of the best colleges in the world. In order to avail for an IIT, you will need to score at least the cutoff percentile in JEE mains following which you will need to give the JEE Advanced exam where you need to have around 7500-8000 rank to get a good branch in an IIT. 

The JEE Mains cutoff for 2019 is - 

Common Rank List - 89.75%

Gen EWS - 78.217%

OBC NCL - 74.316%

SC - 54.012%

ST - 44.344%

PWD - 0.1137%

For government colleges, you can try JOSAA councilling which has quite a few of government colleges. The cutoff of government colleges vary according to branch and college but you can expect to get a good NIT or any other GFTI with about 85+ %.

Hope this helps and best of luck ...

Hello student

The minimum marks to get in to the jee mains NIT government is around  above 120 marks is well and good it is different for different NITs according to their rank or Government engineering College it is also depends on category and competition in that particular year.
So if you mention category also I can help you further more 

All the best