First of all we need to see the previous year closing ranks (via 15% All India Quota) for getting admission in Private MBBS College (Management Seat) -

1. For Private Colleges in Karnataka -

• For a good Private College (a reputed college with good clinical experience and quality education) - Closing AIR - 1,50,000
• For any Private College in Karnataka - Closing AIR - 4,40,000

2. For Any Private College in India, Closing AIR (for General Catorgy) - 6,30,231 (College Allotted - Dr. DY Patil Medical College)

Since cut off varies from year to year (as it depends on difficulty level of question paper, number of candidates, number of newly opened colleges), a safe closing rank (for this year) would be 1,00,000 to get a good Private college in Karnataka.

Alternatively, to predict what all MBBS Colleges (including Private) you can get with your NEET UG Rank, you may use NEET UG College Predictor Tool - https://medicine.careers360.com/neet-college-predictor