The Ashtapradhan (also known as the Council of Eight Ministers) was a key institution in the Maratha Administration. Option 4 is correct. Here`s a detailed reasoning behind this answer:

The Maratha Empire, which existed from the late 17th century to the early 19th century, had a well-organized system of administration, and the Ashtapradhan was a central component of this governance structure. The Ashtapradhan acted as a council of eight ministers who held important portfolios and assisted the Maratha ruler in the decision-making process.

The eight ministers in the Ashtapradhan were:

1. Peshwa: The Peshwa was the prime minister or chief minister of the Maratha Empire. He held significant power and authority, acting as the principal advisor to the ruler.

2. Amatya: The Amatya was responsible for the administration of finances and revenue collection. He managed the treasury, assessed taxes, and played a crucial role in maintaining the economic stability of the empire.

3. Sachiv: The Sachiv served as the secretary or chancellor and was responsible for maintaining official records, managing correspondence, and overseeing the administration of justice.

4. Mantri: The Mantri was the minister of foreign affairs and defense. He handled diplomatic relations, negotiations, and military matters on behalf of the Maratha ruler.

5. Senapati: The Senapati was the commander-in-chief of the Maratha army. He played a pivotal role in military strategy, troop deployment, and ensuring the security of the empire.

6. Sumant: The Sumant was the minister of foreign trade and commerce. He facilitated trade relations, oversaw commercial activities, and maintained the maritime interests of the empire.

7. Nyayadhish: The Nyayadhish was the chief justice and head of the judicial system. He presided over courts, interpreted laws, and ensured the delivery of justice across the empire.

8. Panditrao: The Panditrao was responsible for religious affairs and provided guidance on matters of faith. He supervised religious institutions, performed religious rituals, and maintained harmony among different religious communities.

These eight ministers formed the core decision-making body of the Maratha administration, collectively advising and assisting the ruler in governing the empire efficiently. They were chosen based on their expertise, experience, and loyalty to the Maratha cause.

It`s important to note that the Ashtapradhan was specific to the Maratha Administration and did not exist in the Gupta, Chola, or Vijayanagar administrations. Each of these ancient Indian empires had their own unique administrative structures and systems of governance.