The earliest occurrence of the mantra famous as Gayatri Mantra is found in the following text:

The answer is C, Rig Veda. The Gayatri mantra is the verse addressed to Savitr, the sun god, in Rig Veda 3.62.10, in the family book (Mandala 3) traditionally attributed to sage Vishvamitra. It is set in the Gayatri metre of 24 syllables, which gives the mantra its name.

• Atharva Veda is wrong. It is a later Veda, and its verses echo Rig Vedic material rather than originating it.
• Bhagavad Gita is wrong. It is an epic-period text, composed long after the Rig Veda, and it only refers to Vedic chanting in general terms.
• Manusmriti is wrong. It is a dharmashastra text, far later than the Vedas. It prescribes japa of the Savitri verse, which shows the mantra's continued importance, but it is not the source.

The core concept is the Vedic corpus and its chronological layers: Samhitas, then Brahmanas and Upanishads, then the epics and smritis. Questions on the earliest occurrence of a text or idea test whether you can place it correctly in that sequence. This also matters for Mains answers on the evolution of Vedic religion and the transition to Puranic and bhakti practice.

Trap: Aspirants pick the Gita or Manusmriti because the Gayatri mantra is so widely recited in later Hindu practice. Earliest occurrence is a question about the source text, not about popularity.