The incorrect statement regarding the administration of the Cholas is option 'D' - The royal household was maintained in a very austere manner, typifying the Southern tradition.

Explanation:
The Cholas were a prominent dynasty in South India that ruled from the 9th to the 13th century. They had a well-organized and efficient administrative system that contributed to their long-lasting influence and success. Let's examine each option to understand why option 'D' is incorrect.

a) The king adopted high-sounding titles:
- The Chola kings adopted grand titles to showcase their authority and power. These titles, such as "Chola Maharaja" and "Gangaikonda Chola," were used to emphasize their supremacy and divine right to rule. This practice was prevalent among the Chola rulers and helped in establishing their authority.

b) The raja guru was both the confident and confessor of the royal family:
- The raja guru played a significant role in the Chola administration. They were spiritual advisors and counselors to the royal family. They provided guidance and support in matters of governance, religion, and personal affairs. The raja guru was considered a trusted confidant and played a crucial role in maintaining the stability and welfare of the kingdom.

c) The statues of the dead rulers were worshipped:
- The Cholas practiced ancestor worship, and the statues of deceased rulers were indeed worshipped. The Chola kings believed in the continuity of their lineage and considered their ancestors as powerful and influential beings. They erected statues and temples in honor of their ancestors and worshipped them regularly. This practice was common in the Chola society and helped in maintaining the dynasty's legitimacy and spiritual connection.

d) The royal household was maintained in a very austere manner, typifying the Southern tradition:
- This statement is incorrect. The Chola royal household was known for its grandeur and opulence. They had a well-structured administrative setup with various officials and departments. The royal palace was adorned with exquisite architecture, intricate carvings, and luxurious amenities. The kings and royal family enjoyed a lavish lifestyle, and their court was a center of cultural, artistic, and intellectual activities. The Cholas were known for their patronage of arts and literature, and their court was a hub for renowned scholars, poets, and artists.

In conclusion, option 'D' is incorrect because the Chola royal household was not maintained in an austere manner, but rather it exemplified grandeur and opulence.