Explanation:

Vijaynagar Empire

The kingdom of Vijayanagar was founded by Harihara and Bukka of the Sangama dynasty. Vijayanagar Empire was ruled by four important dynasties and they are:

• Sangama
• Saluva
• Tuluva
• Aravidu

The most famous king of the Vijayanagara Empire was Krishnadeva Raya. 

• Krishnadeva Raya encouraged trade with the western countries. 
• He had a cordial relationship with the Portuguese who had at that time established trade centres on the west coast of India.
• He composed a work on statecraft in Telugu known as the Amuktamalyada.

The administration under the Vijayanagar Empire was well organized. 

• The king enjoyed absolute authority in executive, judicial and legislative matters. He was the highest court of appeal. 
• The succession to the throne was on the principle of hereditary. 
• The king was assisted by a council of ministers in his day to day administration. 
• The Empire was divided into different administrative units called Mandalams, Nadus, sthalas and finally into gramas. 
• The governor of Mandalam was called Mandaleswara or Nayak. 
• Vijayanagar rulers gave full powers to the local authorities in the administration.

Hence only statement 2nd is correct.