Can I pursue M.Sc in maths after B.Tech in mechanical engineering? Which entrance do I need to write for the same?

Yes, you can do it, but according to your Bachelor's degree M.Sc in maths is not a good option. If you want to pursue your Masters, then you can opt for M.Tech in your field which will provide your better career. All the states conduct entrance exam for M.Sc, you can visit their websites according t