Engineering Entrance Exam

You have not written about the category and home state you belongs. However your expected JEE Main AIR is between 50893-56250. Based on the rank, you can get the following NITs under other state quota for general category.
1. NIT Jammu
2. NIT Sikkim
3. NIT Manipur.

You won't be getting any seat in NIT Warangal under GEN-EWS category. You must try for home state NIT. You would get any seat in your home state NIT.

You must have to score between 500-1000 rank for topp IIT's in india or it also depend on the branch of the courses.

Hi, You haven't specified your percentile. If it is above 80 percentile, then LPU makes perfect sense as:
1. It is top 100 ranked institution in the country and top 80 in engineering.
2. It has solid track record of industry interface and curriculum development in last 2 decades.
3. It has over 800 companies visiting the campus for recruitment of the abundant talent. On top of it, you get a chance to avail the scholarships upto 20 % of programme fee as per your performance. Hope this helps
DVD.

Yes, you can get admission to chemical engineering using your MH-CET scores. Check with a few colleges that give admit on the bases of CET you get into those definitely