Can I give only GRE and go for both MS and MBA?

GRE Exam Eligibility

The only eligibility requirement for GRE is the document required to prove your identity. In India, you’ll need a valid passport. You’ll have to get your original passport (not photocopies) which clearly shows your full name, photograph and signature.
No other documentation (like birth certificate, international driving license etc) can be used as an alternate identity proof. They are very strict about this.
Apart from this eligibility requirement, ETS does not set any age, qualification, timing related pre-requisites. However, there will be a range of eligibility criteria set by universities that accept GRE scores. For each of their programs, they may have minimum age, experience and qualification related filters.