The style of painting that flourished under the patronage of the Hoysala kings:

Chola
Chalukya
Hoysala
Mughal

The correct answer is C. Hoysala.

The Hoysala style of painting flourished under the patronage of the Hoysala kings of Karnataka, India, from the 11th to the 14th centuries. It is characterized by its use of bright colors, intricate patterns, and graceful figures. The paintings often depict scenes from Hindu mythology or everyday life.

The Chola style of painting flourished under the patronage of the Chola kings of Tamil Nadu, India, from the 9th to the 13th centuries. It is characterized by its use of bold colors, strong lines, and dynamic compositions. The paintings often depict scenes from Hindu mythology or the lives of the Chola kings.

The Chalukya style of painting flourished under the patronage of the Chalukya kings of Karnataka, India, from the 6th to the 12th centuries. It is characterized by its use of muted colors, delicate lines, and serene compositions. The paintings often depict scenes from Hindu mythology or the lives of the Chalukya kings.

The Mughal style of painting flourished under the patronage of the Mughal emperors of India from the 16th to the 18th centuries. It is characterized by its use of rich colors, intricate patterns, and realistic figures. The paintings often depict scenes from court life or the lives of the Mughal emperors.