If the President of India exercises his power as provided under Article 356 of the Constitution of a particular State, then

The correct answer is: the powers of the Legislature of that State shall be exercisable by or under the authority of the Parliament.

Step-by-Step Explanation:

1. Understanding Article 356 of the Indian Constitution:
Article 356 contains provisions for emergency in case of failure of constitutional machinery in a State. It is commonly referred to as "President's Rule".

2. Key Consequences of Proclamation under Article 356:
When the President issues a proclamation under Article 356(1):
- The President assumes to himself all or any of the functions of the Government of the State and all or any of the powers vested in or exercisable by the Governor or any body or authority in the State (other than the State Legislature).
- Under Article 356(1)(b), the President declares that the powers of the Legislature of the State shall be exercisable by or under the authority of the Parliament.

3. Evaluating the Options:
- State Assembly dissolution: The State Legislative Assembly is not automatically dissolved; it may initially be kept under suspended animation until Parliament approves the proclamation.
- Legislative Powers: The powers of the State Legislature become exercisable by or under the authority of Parliament. Parliament can also delegate the law-making power to the President.
- Fundamental Rights: Article 19 is suspended during a National Emergency under Article 352 (specifically when triggered by war or external aggression), not automatically under Article 356 (President's Rule).

Therefore, the most accurate constitutional statement is that the powers of the Legislature of that State shall be exercisable by or under the authority of the Parliament.