The question asks to identify the statements that are not correct. All three statements provided are factually incorrect based on the constitutional provisions for Panchayati Raj.
Statement I is incorrect: Article 243B of the Constitution mandates a three-tier Panchayati Raj system (village, intermediate, and district levels). However, it also provides an exemption, stating that Panchayats at the intermediate level may not be constituted in a State having a population not exceeding twenty lakhs. Therefore, intermediate-level Panchayats do not exist in all States.
Statement II is incorrect: Article 243F(1)(a) specifies that a person shall not be disqualified for being chosen as, or for being, a member of a Panchayat if he has attained the age of twenty-one years. There is no requirement for a minimum age of thirty years to be a member of a Panchayat at any level, including the intermediate level.
Statement III is incorrect: Article 243-I of the Constitution stipulates that the Governor of a State shall constitute a Finance Commission every fifth year to review the financial position of the Panchayats and to make recommendations regarding the distribution of net proceeds of taxes, duties, tolls, and fees leviable by the State between the State and the Panchayats. The Chief Minister does not constitute this commission.
Since all three statements (I, II, and III) are incorrect, option (4) is the correct answer as it identifies all non-correct statements.
Options (1), (2), and (3) are incorrect because they suggest that one or more of the given statements are factually correct. As established, all three statements (I, II, and III) are inconsistent with the constitutional provisions related to Panchayats.