Hi
The number of seats available for admissions under management quota is highly subjective to the admissions trend of the current year.
However in most of the private colleges there are atleast 5% - 10% of seats reserved for admissions under management quota. The best that you can do at the moment is shortlist the colleges you are seeking admissions into and thereafter check with those college's admissions office so as to what is the process like and how many seats have they kept for admissions under management quota this year. Also if you are looking for admissions under management quota, then the sooner you start the process the better it is because bookings for seats under management quota starts quite in advance.

There's not any particular number of seats, the seats may vary every year. Currently, there are 8 private colleges which offering 560 BSc nursing seats among which most of the seats are reserved for government exams and some seats are available for management quota. I suggest you to wait for counseling to get more information about this.
Hope it helps.
Thank you.