The correct answer is: C. chief justice of the state high court.
The oath of office is administered to the members of state council of ministers by the chief justice of the state high court. This is because the chief justice is the highest judicial officer in the state and is responsible for upholding the law. The oath of office is a solemn promise that the members of the state council of ministers will uphold the Constitution and the laws of the state.
Option A is incorrect because the governor is the head of state of the state and is not responsible for administering the oath of office to the members of the state council of ministers.
Option B is incorrect because the chief minister is the head of government of the state and is not responsible for administering the oath of office to the members of the state council of ministers.
Option D is incorrect because the speaker of the legislative assembly is the presiding officer of the legislative assembly and is not responsible for administering the oath of office to the members of the state council of ministers.