how can I get job in private sector with good salary after msc chemistry without any exam?
If you do MSc from any university that offers campus placement then you will partially have to give no exam but a interview. This can be a way out.
For any thing else you have to give an interview by seeing the vacancies in the company you want to take part in. Register in online job website like Linkedin or Naukri etc and build your profile with proper skills and requirements. If you will be short listed you will be called for an interview. If you get selected in that interview you can get the job.
I hope my answer helps. All the very best for your future endeavors!