Option 1: Co-ordinate Authority refers to a situation where the State Government and local government work together in a coordinated manner. It means that both entities have equal power and authority.

Option 2: Delegated Authority is the correct answer. It means that the State Government delegates or transfers some of its authority and powers to the local government. This allows the local government to make decisions and take actions within their jurisdiction.

Option 3: Superior Authority suggests a situation where the State Government has superior or greater authority over the local government. This means that the State Government can override or supersede any decisions made by the local government.

Option 4: Independent Authority implies that the local government has complete independence from the State Government. It means that the local government has full control and authority without any interference from the State Government.

In summary, the correct answer is option 2: Delegated Authority, as it explains the relationship between the State Government and the local government where the State Government transfers some of its authority to the local government.