If you want to hunt for a job in Mumbai, your only option would be to arrive on a tourist visa. See “You want to go on reconnaissance.” The problem is tourist visas are only for people coming to India for tourism or other non-business purposes – showing up in Mumbai to apply for jobs and seek interviews is technically business related. Plus, you cannot work on a tourist visa in India.
It is probably a better idea to secure a job from abroad first. If the company offers you a “look-see” before you sign a contract, you could then go to India on a tourist visa to get a feel for the place before making your final decision.
To work in India you need an employment visa. See “You have a job and need to relocate.”