The Nayaka kingdom known for its patronage of literature and arts:

Nayakas of Madurai
Nayakas of Chitradurga
Nayakas of Keladi
Nayakas of Tanjore

The correct answer is: D) Nayakas of Tanjore.

The Nayakas of Tanjore were a Telugu dynasty that ruled over the region of Tamil Nadu in southern India from the 16th to the 18th centuries. They were known for their patronage of literature and arts, and their kingdom was a center of cultural activity.

The Nayakas of Tanjore were founded by Vira Narasimha Raya, who was a general in the Vijayanagara Empire. After the fall of the Vijayanagara Empire in the 16th century, the Nayakas of Tanjore became independent rulers. They ruled over a large territory that included the modern-day districts of Tanjore, Tiruchirapalli, Pudukkottai, and Ramanathapuram.

The Nayakas of Tanjore were patrons of literature and arts. They built many temples and palaces, and they commissioned many works of art. The Nayaka period is considered to be a golden age of Tamil literature and art.

Some of the famous works of literature that were written during the Nayaka period include the Tirukkural, the Nala Damayanti, and the Kamba Ramayana. Some of the famous works of art that were created during the Nayaka period include the Chola bronzes, the Nayaka paintings, and the Nayaka architecture.

The Nayakas of Tanjore were overthrown by the British in the 18th century. However, their legacy continues to live on in the form of the many temples, palaces, and works of art that they commissioned.