Introduction:
The Indian Constitution provides for a system of checks and balances to ensure the smooth functioning of the government. One such mechanism is the power of veto, which allows the President and the Governor to prevent the enactment of a law. In this context, the given statements are to be evaluated for their accuracy.

Statement 1: Veto Power of the President of India is guided by Article 111 of the Indian Constitution.

Explanation:
Article 111 of the Indian Constitution deals with the 'Assent to Bills' by the President. It states that when a Bill is presented to the President for his assent, he may either give his assent or withhold it. If the President gives his assent, the Bill becomes law, but if he withholds his assent, it does not become law. This power to withhold assent is known as the veto power.

The President can exercise three types of veto powers:
1. Absolute Veto: The President can refuse to give his assent to any Bill, and in such a case, the Bill does not become law.
2. Suspensive Veto: The President can return the Bill for reconsideration to the Parliament. If the Parliament passes the Bill again with or without amendments, the President is bound to give his assent to it.
3. Pocket Veto: The President can keep a Bill with him without giving his assent or withholding it, and in this case, the Bill does not become law.

Therefore, the statement that the veto power of the President of India is guided by Article 111 of the Indian Constitution is correct.

Statement 2: Article 112 of the Indian Constitution deals with the powers of the Governor with regard to assent given to bills passed by the State legislature.

Explanation:
The statement is incorrect. Article 112 of the Indian Constitution does not deal with the powers of the Governor with regard to the assent given to bills passed by the State legislature. Article 112 pertains to the 'Annual Financial Statement' or the budget presented by the President of India. It specifies that the President shall cause to be laid before both Houses of Parliament the Annual Financial Statement.

The powers of the Governor with regard to the assent given to bills passed by the State legislature are mentioned in Article 200 of the Indian Constitution. According to Article 200, when a Bill is presented to the Governor for his assent, he can give his assent, withhold his assent, or reserve the Bill for the consideration of the President. If the Governor reserves the Bill for the consideration of the President, the President can either give his assent or withhold his assent. If the President gives his assent, the Bill becomes law, but if he withholds his assent, it does not become law. The Governor's powers with regard to assent given to bills are similar to those of the President.

Conclusion:
In conclusion, statement 1 is correct as the veto power of the President of India is guided by Article 111 of the Indian Constitution. However, statement 2 is incorrect as Article 112 of the Indian Constitution does not deal with the powers of the Governor with regard to the assent given to bills passed by the State legislature.