Investment in NRE Fixed deposits
This should be the first choice of investment for a NRI. This is because NRE deposits are easily repatriable and income from interest on NRE tax deposits is exempt from tax. NRE deposits can be broken and transferred to the NRE savings account, where they can be easily repatriated. Interest on NRE fixed deposits are currently the same like those for resident Indian deposits. The big difference being that NRE fixed deposits are tax free.
Investment in government bonds and securities
Non Resident Indians are permitted to invest in government securities and bonds. However, such investment should be done for a minimum of 3 years. If such investments are purchased from NRE/FCNR account, the same accounts would be credited on sale of these instruments and hence maturity proceeds can be repatriated.
Investment in mutual funds
Investment in mutual funds can be done by Non Resident Indians only through NRI/NRO/FCNR account or through "inward remittance". If NRIs are looking to repatriate the amount, one should invest for at least 3 years period.
Investment in NRO fixed deposits
Non Resident Indians can also look to invest in NRO fixed deposits, but, it would not be sensible to do so. With interest rates on NRE fixed deposit and NRO fixed deposit the same, it would be prudent to invest in NRE fixed deposits, simply because they are tax free, while interest on NRO fixed deposits are not tax free.