Consider the following statements: [State Legislature & Executive]

I. The Constitution of India/explicitly mentions that in certain spheres the Governor of a State acts in his/her own discretion.
II. The President of India can, of his/her own, reserve a bill passed by a State Legislature for his/her consideration without it being forwarded by the Governor of the State concerned.

Which of the statements given above is/are correct?

The correct option is I only.

Let us analyze each statement step-by-step to understand why this is the correct answer:

Statement I: The Constitution of India explicitly mentions that in certain spheres the Governor of a State acts in his/her own discretion.
Unlike the President of India, who is generally bound by the aid and advice of the Council of Ministers (Article 74), the Constitution of India explicitly makes room for the Governor of a State to act in their own discretion under Article 163(1). Article 163(1) states that there shall be a Council of Ministers with the Chief Minister at the head to aid and advise the Governor in the exercise of his functions, except in so far as he is by or under this Constitution required to exercise his functions or any of them in his discretion. This constitutional provision explicitly mentions the discretionary powers of the Governor. Therefore, Statement I is correct.

Statement II: The President of India can, of his/her own, reserve a bill passed by a State Legislature for his/her consideration without it being forwarded by the Governor of the State concerned.
According to Article 200 of the Constitution of India, when a Bill has been passed by the Legislative Assembly of a State or, in the case of a State having a Legislative Council, by both Houses of the Legislature of the State, it must be presented to the Governor. It is the Governor who decides to either give assent, withhold assent, return the bill (if it is not a Money Bill), or reserve the bill for the consideration of the President. The President of India cannot, of his or her own initiative, directly bypass the Governor and reserve a state bill for his or her own consideration. The bill must be forwarded/reserved by the Governor first. Therefore, Statement II is incorrect.

Hence, only Statement I is correct.