Am I eligible to take part in JOSAA with 76 marks in JEE Mains from open category as the cut-off trend was 81 for the year?

Amrut Institute offer admission in BTech and Diploma in Engineering based on merit in last qualifying exam. So, no JEE Main is not compulsory to take admission in Amrut Institute courses. 

With 57.8 percentile in JEE Main and 73% boards, getting CSE/AI in top government colleges is unlikely. But you still have good chances in private colleges through UPTAC/AKTU or direct admission.

Possible options:

KIET Group of Institutions

ABES Engineering College

Galgotias Coll

JEE (Main) cutoff for BTech in Computer Science and Engineering in Sagar Institute of Science Technology and Research, Bhopal in the closing round has ranged between 3,75,232 to 10,07,060 from 2021 to 2023.

Yes, you can get admission in BTech in Sagar Institute of Science Technology and Research without JEE (Mains) rank through College Level Counselling based on merit if there are any seats left vacant after DTE Bhopal Counselling.

Yes, students can get EIT Faridabad scholarship with 97.6 percentile in JEE Main. Applicants can get scholarship on the basis of scores in entrance exam. Check the table below to know eligiblity of scholarships offered on the basis of JEE Main scores: