You need to appear JEE Mains in order to take admission into NITs and IIITs

The list of exams

1)Jee Mains ( But you need more than 240 marks) 
2)Go to the website for IIIT HYD. There is a CLD and CND exam based on qualification
3)SAT (WITH SCIENCE AND LANG PAPERS)
4)If you aren't an Indian citizen the you get direct entry.

However these exams portals have been closed,  so if you really  want to try I suggest writing SAT.  Please go to the website for further  details

Hope this helps...
:-D