See the pay levels of the private autonomous colleges aren't fixed. Its dependent on the status of the college and its reputation. Sometimes in Private college considerable increments aren't given and there can be sometimes that the recruitment is entirely contractual which fixes the salary and a little increment for a period. So in general its hard to say so. But as per some of the top online recruitment platforms the salary after 7 years of experience can vary in the range of Rs. 60k-1L at most in most of the Private colleges. Now if you have done PHD from abroad or have been a professor in some college of higher repute compared to that of the private college then you can get moreover like Rs. 1.5L at max per month.

I hope this answer helps. All the very best for your future endeavors!