What should I do to pursue further studies from the cities like Delhi and Mumbai?

You must look up for the list of colleges of Delhi and Mumbai that are of your interest, and check if they have got any entrance exam for further level of studies that you wish to pursue. If not, you may have to go through the minimum eligibility criteria specified by that university. Eg. IIT Bombay

Hello Shubham, You have reasonable marks in Chemistry. You can think of pursuing M.Sc in chemistry. There are lots of possibilities after this. Follow what your heart says.