The correct options for the epithets of Gautama Buddha are 2 (Shakyamuni) and 3 (Tathagata). "Shakyamuni" means "the sage of the Shakyas," referring to the Buddha's lineage from the Shakya clan, while "Tathagata" signifies "one who has thus gone" or "one who has thus come," highlighting his enlightened state. In the context of UPSC Prelims, understanding these epithets is crucial as they reflect not only the historical significance of Buddha but also the philosophical concepts underpinning Buddhism, which are often examined in relation to India's socio-cultural evolution during ancient times.