Hello Gouri,
No, there is no cutoff for management seats in Amrita or in any other college or university. You need to pay the management fees to get a seat for yourself for the course you want admission in. With the help of management, anyone can get admission directly with no merit score. But the fees of management quota are high and every college charges as per their own requirements,
I hope this helps you out. If there is anything else that I can help you with, then please let me know.
Till then, all the very best. Stay home and stay safe.