Hi Raghunath Vishnubhotla,

Based on your rank and caste and branch you pick they will allot a particular college to you , so i request you to please mention caste so to help you in better way and coming to your question based on your rank  , you have very good chances to get admission iin Amrita university as per previous year cut off rank is 6767  so try your luck and for more information go to below link

https://engineering.careers360.com/articles/aeee-cutoff

and to know about college go to

https://www.careers360.com/university/amrita-vishwa-vidyapeetham-coimbatore

Hope this information is helpful

ALL THE BEST