Hey Harsh, You have scored 95 percentile and your rank is 14k. You might belong to some reserved category then your rank is too high with this percentile. Yes, you can take admission in NITs with this rank for Mechanical Engineering and Electrical Engineering and it would be best for you to take admission there. If you want to check various colleges you can check at JEE MAINS COLLEGE PREDICTOR and choose the best one for you so as to get seat in best college.

https://engineering.careers360.com/jee-main-college-predictor?icn=jeemain-cp&ici=qna-sticky-wap

Yes there is many chances but don't expect good ranking nit such as nit Allahabad.