Concept:
The Vijayanagara Empire was founded in 1336 by the brothers Harihara and Bukka in the Krishna-Tungabhadra doab.
While modern historians universally designate the polity as the 'Vijayanagara Empire' after its imperial capital, contemporary inscriptional and literary sources used an indigenous regional title.
Step 1: Examining Contemporary Terminology:
Contemporary epigraphic records, royal grants, and literary texts in Telugu, Kannada, and Sanskrit referred to the state as the Karnataka Samrajyamu (the Empire of Karnataka).
This designation underscored the core cultural, linguistic, and territorial heartland in which the political power of the Sangama dynasty initially emerged.
Conversely, contemporary foreign travelers and European chroniclers commonly referred to the polity simply by the name of its grand capital city, Vijayanagara (the 'City of Victory'), or as the kingdom of Narsinga.
Step 2: Evaluating the Other Options:
Option (A) Tamilkam refers to the ancient cultural realm of the Tamil country during the Sangam era.
Option (C) Vijayanagara Samrajyamu is the terminology applied predominantly by modern twentieth-century historians.
Option (D) Kerala Samrajyamu refers to the southwestern littoral Chera/Malayalam territory.
Final Answer:
Contemporaries described the Vijayanagara Empire as the Karnataka Samrajyamu.