Yes, you need Passport to take GRE exam at any GRE testing center in India. Passport if the only identification proof which GRE exam centers accept. Drivers licence is not valid at testing centers in India.
But to register for the GRE exam online, you don't need a Passport number. You can book GRE exam date without passport.
If you are planning take GRE,TOEFL tests, it is always safe to apply to passport early.
"Testing in Bangladesh, India, Pakistan and Nigeria:
You MUST present a valid passport with your name, photograph and signature as your primary ID document. There are no exceptions to this policy."
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