As an individual you do not need to take RBI permission for investing in mutual funds. You can invest through repatriable or non repatriable basis and there is no limit upto which you can invest in mutual funds. but you are not eligible to invest in any mutual fund scheme.
NRIs can invest by way of capital contribution in any proprietary or partnership concern in India provided the firm or the proprietary concern is not engaged in any agricultural/plantation activities or real estate business or Print Media on non-repatriation basis subject to the certain conditions.
NRIs/OCBs as been ranted general permission to subscribe to the shares/convertible debentures of an Indian company on non-repatriation basis, and to an Indian company to issue shares or convertible debentures by way of new/rights/bonus issue to NRIs/OCBs on non-repatriation basis provided that the investee company is not engaged in agricultural/plantation activities or real estate business (excluding real estate development i.e. development of property or construction of houses) or chit fund or is not a Nidhi company.