Among the following rivers, which one is not mentioned in the hymns of the Rigveda, the earliest Vedic text of ancient India?

Introduction / Context:
This question relates to the geography of the Vedic age as reflected in the Rigveda, the oldest of the Vedic texts. The Rigvedic hymns mention several rivers of northwestern and northern India, which helps scholars reconstruct the area where the Vedic people lived. The question asks which river among the options is not mentioned in the Rigveda at all, testing both knowledge of Vedic geography and familiarity with Indian rivers in general.

Given Data / Assumptions:
- The question is restricted to rivers mentioned in the Rigveda.
- The options include Sindhu, Saraswati, Yamuna, Periyar and Gomti.
- We assume the standard scholarly consensus that the Rigveda describes mainly rivers of the northwestern region, not peninsular rivers like Periyar.

Concept / Approach:
The Rigveda frequently mentions the Sindhu river and its tributaries. It also praises the Saraswati river and refers, though less often, to rivers like Yamuna. The Vedic geography focuses on the northwestern part of the subcontinent. Periyar, on the other hand, is a major river of southern India, flowing in Kerala, and lies far outside the Vedic heartland described in the Rigveda. Therefore, a good strategy is to identify which river does not belong to the northwestern or northern region and hence is unlikely to be named in the Rigvedic hymns.

Step-by-Step Solution:
Step 1: Recognise that Sindhu is simply another name for the Indus river, which is one of the most prominent rivers in the Rigveda. Step 2: Recall that Saraswati is praised in several Rigvedic hymns as a mighty and sacred river. Step 3: Remember that Yamuna, although less prominent than Saraswati or Sindhu, is also mentioned in the Rigveda. Step 4: Note that Periyar is a river of southern India in the present state of Kerala and is not part of the northwestern Vedic river system. Step 5: Based on this regional and textual logic, identify Periyar as the river not mentioned in the Rigveda.

Verification / Alternative check:
To verify, you can mentally list the rivers most frequently appearing in Rigvedic discussions: Sindhu, Saraswati, Ravi, Beas, Sutlej, and others in the Punjab region, along with some mention of Yamuna and Ganga. All of these belong to the north or northwest. When you contrast this with Periyar, which flows entirely in the far south, it becomes clear that it is not a Rigvedic river. Textual analysis by historians consistently confirms that Periyar is absent from Rigvedic references.

Why Other Options Are Wrong:
Sindhu: Central to Rigvedic hymns; the very name Hindustan is indirectly related to this river.
Saraswati: Highly praised in the Rigveda and described as a mighty river and goddess.
Yamuna: Mentioned in the Rigveda, though not as frequently as Sindhu or Saraswati.
Gomti: While not as prominent as Sindhu or Saraswati, it is part of the northern river system and not the southern region like Periyar, and is more consistent with the Vedic geographic sphere than Periyar.

Common Pitfalls:
Some students may not be fully familiar with the location of Periyar and might choose Yamuna or Gomti by mistake. Another error is assuming that only the famous Ganga and Yamuna were known in the Rigvedic period, overlooking Sindhu and Saraswati, which are actually more central in Rigvedic hymns. Carefully linking the Rigveda with the northwestern geography and recognising Periyar as a southern river helps avoid confusion.

Final Answer:
The river that has no mention in the Rigveda is Periyar.