The Hoysala king famous for his military campaigns and temple-building activities:

Ballala II
Veera Ballala III
Vishnuvardhana
Vinayaditya

The correct answer is: C) Vishnuvardhana.

Vishnuvardhana was the founder of the Hoysala Empire in 1004 CE. He was a great warrior and a patron of the arts. He built many temples, including the famous Halebidu temples.

Ballala II was the son of Vishnuvardhana. He was a great warrior and a successful ruler. He defeated the Chola king Rajendra Chola I in the Battle of Takkolam in 1067 CE.

Veera Ballala III was the grandson of Vishnuvardhana. He was a great warrior and a successful ruler. He defeated the Chola king Kulottunga Chola I in the Battle of Sorab in 1116 CE.

Vinayaditya was the great-grandson of Vishnuvardhana. He was a great warrior and a successful ruler. He defeated the Chola king Vikrama Chola I in the Battle of Talakad in 1121 CE.

Vishnuvardhana was the most famous Hoysala king because of his military campaigns and temple-building activities. He was a great warrior who defeated many enemies, including the Chola kings. He was also a patron of the arts and built many temples, including the famous Halebidu temples.