The correct option is (a).
Explanation
The office of the Chief Minister functions as the real executive authority in the state administration, operating within the framework of the parliamentary system where the executive is responsible to the legislature.
Statement 1 is Correct:
In a parliamentary democracy, the Chief Minister is appointed by the Governor, typically being the leader of the party or coalition that commands a majority in the State Legislative Assembly. As the head of the government, the Chief Minister acts as the leader of the ruling party’s Members of the Legislative Assembly (MLAs) and usually functions as the Leader of the House (if they are a member of the Assembly).
Statement 2 is Incorrect:
The Chief Minister is not legally or constitutionally bound to resign merely based on a demand from the Opposition. The tenure of the Chief Minister depends on the "pleasure of the Governor," which is practically determined by the majority support in the Legislative Assembly. Resignation becomes mandatory only if the government loses a No-Confidence Motion or fails to prove its majority on the floor of the House.
Key Takeaway:
The Chief Minister’s tenure is secured by the confidence of the Legislative Assembly, not by the political demands of the Opposition. Removal requires a formal loss of majority through a floor test.