The question is about the National e-Vidhan Application (NeVA) and asks us to identify which statements are correct based on given options.

1. Let's analyze the first statement: "It is a Mission Mode Project (MMP) under the Digital India Programme (DIP) of the Government of India."
   • This statement is correct. NeVA is indeed a Mission Mode Project under the Digital India initiative, aiming for the digital transformation of legislative operations.
2. The second statement is: "This application is based on the principle of 'One Nation – One Application'."
   • This statement is also correct. NeVA is designed to provide a unified digital platform for all legislative bodies in India, aligning with the 'One Nation – One Application' principle.
3. Next, consider the third statement: "It has been developed by the Parliament Secretariat."
   • This statement is incorrect. The National Informatics Centre (NIC) has developed NeVA under the Ministry of Parliamentary Affairs, not the Parliament Secretariat.
4. Finally, the fourth statement: "Its core aim is for end-to-end digitalisation of all the functions of the State Legislatures."
   • This statement is correct. NeVA's main objective is to digitally transform all functions of State Legislatures to streamline and enhance their operation.

Given the analysis above, the correct statements are 1, 2, and 4. Therefore, the correct answer is the option that includes statements 1, 2, and 4.