Preparing for a government exam parallel with M.Sc Chemistry, is a bit tough. Here are some reasons as to why it could become difficult.
If you have free time, utilize it by visiting the library and reading books on inorganic chemistry. You could also complete your assignments to stay a bit ahead.
You will be left with 4-5 hours because of your M.Sc. but it is still sufficient, as you can study effectively between these hours. Make short notes and focus one day on revision, do mock tests to analyze your strengths and weaknesses and work on them.