I have got 51000 rank in jee mains. can I get any NIT or IIIT?

With 51000 rank in general category, it would be difficult to get top branches in any NIT as the CSE seats of those NITs lie around 3000-4000 rank in top NITs, average NITs has get filled within 8000 to 10000. It would be difficult to get top branches such as Computer science or Electronics etc. Based on your rank and considering you as a general category student, you can expect CSE in NITs such as Silchar, Uttarakhand, Srinagar, Hamirpur and North East NITs etc. And other branches such as Civil, Electrical, Electrical and Electronics Engineering, Production etc in NITs like Patna, Silchar, Raipur etc. And you haven't mentioned your Home state quota, your category too a sthe cutoffs for home state candidates are quite less compared to All India quota. However this is based on previous years' data and this year it might change. You can predict your college through our Jee Main College Predictor tool http://engineering.careers360.com/jee-main-college-predictor?icn=QnA&ici=qna_answer
Check the cutoffs here http://engineering.careers360.com/articles/nits-cutoff-for-top-btech-branches
http://engineering.careers360.com/articles/jee-main-cutoff-for-top-iiits