Hello Aspirant.

Comgratulations on securing good JEE main percentile and AEEE ranks. Amrita University is indeed a good backup choice if you're aiming for NIT's. For your rank, you can get a seat of your choice in any amrita University (which is based on Previous year rankings). However, you cant avail a scholarship since its only provided for top 2k ranks. For your reference . I'll attach you two links , one for courses and rankings and other is for fee structure.

Refer:

Https://www.amrita.edu/admissions/btech-2019/fee-structure

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

Hope that helps

All the best