Explanation:

Option 1, Article 257, is correct as it shapes the relationship between the center and states in India, addressing the principal of federalism. This article states that the executive power of every state shall be so exercised as not to impede or prejudice the exercise of the executive power of the Union.

Option 2, Article 258, relates to the power of the Union to entrust functions to the State with consent. While it does concern State and Union relations, it does not specifically discuss the careful exercise of state power to avoid impeding Union power.

Option 3, Article 355, declares the duty of the Union to protect states against external aggression and internal disturbance. It does not address the particular use of state`s executive powers like Article 257 does.

Option 4, Article 356, references a situation when state government cannot be carried on in accordance with the provisions of the Constitution, leading to President`s rule. This is not directly related to the conservative exercise of state`s executive powers to not hamper Union`s power. Hence, it`s not the right answer.