Which famous temple is located in Thanjavur?

Brihadishvara Temple 

The correct answer is Option (2) → Brihadishvara Temple 

Brihadishvara Temple is located in Thanjavur.

According to tradition and epigraphic evidence two brothers, Harihara and Bukka, founded the Vijayanagara Empire in 1336. This empire included within its fluctuating frontiers peoples who spoke different languages and followed different religious traditions.

On their northern frontier, the Vijayanagara kings competed with contemporary rulers – including the Sultans of the Deccan and the Gajapati rulers of Orissa – for control of the fertile river valleys and the resources generated by lucrative overseas trade. At the same time, interaction between these states led to sharing of ideas, especially in the field of architecture. The rulers of Vijayanagara borrowed concepts and building techniques which they then developed further.

Some of the areas that were incorporated within the empire had witnessed the development of powerful states such as those of the Cholas in Tamil Nadu and the Hoysalas in Karnataka. Ruling elites in these areas had extended patronage to elaborate temples such as the Brihadishvara temple at Thanjavur and the Chennakeshava temple at Belur. The rulers of Vijayanagara, who called themselves rayas, built on these traditions and carried them, as we will see, literally to new heights.