I. There shall be a public service commission for the Union and a Public Service commission for each state.
The answer is: C
Explanation
The correct option is C: I and II.
According to Article 315 of the Indian Constitution, both statements I and II are correct. Statement I states that there shall be a public service commission for the Union and a public service commission for each state. This is true, as Article 315(1) establishes the Union Public Service Commission (UPSC) and the State Public Service Commissions for the recruitment and appointment of civil servants at the central and state levels respectively.
Statement II states that the public service commission for the Union, if requested to do by the governor of a state may, with the approval of the president, agree to serve all or any of the needs of the state. This is also true, as Article 315(4) allows the UPSC to serve the needs of a state, with the consent of the governor and the president, if requested by the state. This provision enables the UPSC to assist the state governments in matters of recruitment, promotion, disciplinary actions, etc. of their civil servants.