Under which Article does the Governor appoint the Chief Minister of a state?

It provides that the Governor of a state shall be appointed by the President by warrant under his hand and seal, which is why a Governor is not elected and owes his office to the Union executive.

The Rajasthan Legislative Assembly has two hundred seats filled by direct election from territorial constituencies, and the figure matters for a second reason: the Council of Ministers may not exceed fifteen per cent of that strength, which gives a ceiling of thirty ministers including the Chief Minister.

Parliament may by law create a Legislative Council for a state that does not have one, or abolish one that does, if the Legislative Assembly of that state first passes a resolution by a majority of its total membership and by two thirds of the members present and voting.

Article 159 requires the Governor, before entering upon his office, to make and subscribe an oath in the presence of the Chief Justice of the High Court of that state, or in his absence the senior-most judge of that court available.

Article 164(1A), inserted by the Ninety-first Constitutional Amendment of 2003, provides that the total number of ministers including the Chief Minister shall not exceed fifteen per cent of the total strength of the Legislative Assembly, and fifteen per cent of Rajasthan's two hundred seats is thirty.