The correct answer is option 'C' - Brahmanas.

Explanation:
The royal sacrifices of Rajasuya, Asvamedha, and Vajapeya are mentioned for the first time in the Brahmanas. Let's understand what the Brahmanas are and how they relate to these sacrifices.

1. Brahmanas:
The Brahmanas are a collection of prose texts that form part of the ancient Indian scriptures known as the Vedas. They provide detailed explanations and instructions for the rituals and sacrifices described in the Vedic Samhitas.

2. Vedic Samhitas:
The Vedic Samhitas are the oldest layer of the Vedas and include collections of hymns and prayers. They form the foundation of the ancient Indian religious and philosophical traditions.

3. Royal Sacrifices:
The royal sacrifices of Rajasuya, Asvamedha, and Vajapeya were elaborate rituals performed by kings to assert their power and establish their supremacy. These sacrifices were considered highly prestigious and were performed to gain divine blessings, prosperity, and superiority over other rulers.

4. Mention in the Brahmanas:
The Brahmanas, being the explanatory texts of the Vedic Samhitas, provide detailed descriptions and instructions for the performance of various rituals and sacrifices. It is in these texts that the royal sacrifices of Rajasuya, Asvamedha, and Vajapeya are first mentioned.

By studying the Brahmanas, one can gain a deeper understanding of the rituals and sacrifices described in the Vedic Samhitas. These texts provide insights into the religious and social practices of the ancient Indian society and shed light on the importance of these royal sacrifices in establishing and maintaining the authority of kings.

In conclusion, the Brahmanas mention the royal sacrifices of Rajasuya, Asvamedha, and Vajapeya for the first time. These texts provide detailed explanations and instructions for these elaborate rituals, which were performed by kings to assert their power and gain divine blessings.