The correct answer is option 3 - Tamil, Telugu, and Sanskrit. The rulers of Vijayanagar promoted the use of these languages during their reign. This suggests that these languages were given importance and support by the ruling elite.

Tamil, one of the oldest languages in the world, has a rich literary tradition and was the language of the common people in this region. Telugu was another prominent regional language spoken by a large population. Sanskrit, on the other hand, was considered a classical language and was used by scholars and intellectuals. The rulers of Vijayanagar recognized the cultural and linguistic diversity of their kingdom and encouraged the development of these languages to preserve and promote the local traditions and identities.