The Constitution of India does explicitly mention that in certain spheres, the Governor of a State acts in his/her own discretion. This is supported by Article 163, which provides that the Governor is required to act on the advice of the Council of Ministers, except in matters where discretion is allowed by the Constitution. Therefore, Statement I is correct. Regarding Statement II, the President of India cannot, on his/her own, reserve a bill passed by a State Legislature for consideration. The process involves the Governor of the State reserving the bill for the President's consideration, as per Article 200 and Article 201 of the Indian Constitution. The President acts on the bill only after it has been reserved by the Governor. Therefore, Statement II is incorrect.