NRIs can invest in Indian mutual funds through an NRE or NRO bank account, using either repatriable or non-repatriable routes depending on the account and source of funds. KYC must reflect your NRI status and current overseas address.
The main practical friction point is for NRIs based in the US and Canada — many Indian AMCs restrict or place extra conditions on investments from these two countries due to FATCA-related compliance costs, though a growing number now accept them with additional documentation.
Beyond the account and paperwork, the fund selection question is the same as for resident Indians: goal, time horizon and risk should drive the category, not the fact that you’re investing from abroad.