According to the Fifth Schedule of the Indian Constitution, the executive power of a State extends to the Scheduled Areas within its territory. This means that the State Government does not lose its executive power in such areas, and a local body does not assume total administration, which makes statement I incorrect. Furthermore, while the Governor of a State with Scheduled Areas is required to make reports to the President regarding the administration of these areas, the Union Government does not take over the total administration of such areas. Instead, the Union Government can give directions to the State regarding the administration of these areas, but it does not assume total control, making statement II incorrect as well. Therefore, neither statement I nor II is correct.