Is there a management quota offered by Fergusson College for FYBA admissions?

Yes, some of the first-year courses at Fergusson have a management quota. Generally, it is 15% of all seats. Although the cut-off is not very huge for Fergusson so you may get an admission based on merit itself. You may have to wait till the third or fourth list but it is definitely possible and doable.

This donation amount varies from college to college, the more popular the college the bigger the donation amount. Private colleges in India have some seats reserved for the management quota. This could be anywhere between 5-20%. 

Admission to these seats is made on the decision of the college and their selection criteria. Management Quota is for those students, who are unable to get admission through the entrance examinations.