The correct statements about Pradhan Mantri Gram Sadak Yojana (PMGSY) are:

1. It is a centrally sponsored scheme.

   • Correct. PMGSY is a centrally sponsored scheme, where both the central and state governments contribute funds.

2. Rural roads are in the state list as per the Constitution.

   • Incorrect. Rural roads are in the Concurrent List of the Constitution, which means both the central and state governments can legislate on the subject.

3. It aims to connect eligible unconnected habitations as per the core network with a population of 250 persons and above with all-weather roads.

   • Correct. The main objective of PMGSY is to provide all-weather road connectivity to eligible unconnected habitations with a population of 250 persons and above.

So, the correct statements are 1 and 3.