Under the Indian Constitution, the distribution of powers and functions between the Union and the States is clearly defined. The conduct of business of the Government of a State, the Council of Ministers to aid and advise the Governor, and the duties of the Chief Minister are all important aspects of the functioning of the State Government. Let's examine each of these provisions in detail to understand why option 'C' is the correct answer.

1. Conduct of business of the Government of a State - Article 166:
Article 166 of the Indian Constitution deals with the conduct of business of the Government of a State. It states that the Governor of a State shall conduct the business of the State Government in accordance with the rules of procedure made by the Governor himself. The Governor is required to act with the aid and advice of the Council of Ministers headed by the Chief Minister in the exercise of his functions, except in cases where he is required to act in his discretion. This article ensures the smooth functioning of the State Government.

2. Council of Ministers to aid and advise Governor - Article 164:
Article 164 of the Indian Constitution provides for the Council of Ministers to aid and advise the Governor. It 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 cases where he is required to act in his discretion. The Council of Ministers is collectively responsible to the State Legislature and its advice is binding on the Governor. This article establishes the democratic principle of collective responsibility and ensures that the Governor does not exercise arbitrary power.

3. Duties of Chief Minister - Article 167:
Article 167 of the Indian Constitution deals with the duties of the Chief Minister of a State. It states that it shall be the duty of the Chief Minister to communicate to the Governor of the State all decisions of the Council of Ministers relating to the administration of the affairs of the State and proposals for legislation. The Chief Minister also provides information to the Governor regarding the decisions of the Council of Ministers. This article establishes the role and responsibilities of the Chief Minister in the State Government.

In conclusion, all three provisions mentioned in the options are correctly matched. Article 166 deals with the conduct of business of the Government of a State, Article 164 establishes the Council of Ministers to aid and advise the Governor, and Article 167 outlines the duties of the Chief Minister. Therefore, option 'C' - 1 and 3 Only, is the correct answer.

Article No. 163 - Council of Ministers to aid and advise Governor Article 164 - Other provisions as to Ministers Article 166 - Conduct of business of the Government of a State Article 167 - Duties of Chief Minister