River Ganges is ______ largest river in India.

Concept. In English, a superlative adjective (the form ending in ‑est or formed with ‘most’, e.g. largest, tallest, most important) names a one-of-a-kind item — the single highest-ranked thing in its group. Because such an item is unique, it is always introduced by the definite article “the”: the + superlative.

Application.

1. The blank sits directly before “largest”, which is the superlative of “large”.

2. A superlative singles out one unique item, so it requires the definite article, not an indefinite one.

3. Therefore the slot must be filled by “the”, giving “River Ganges is the largest river in India.”

Contrast. The indefinite articles “a” / “an” introduce one non-specific member of a class (a river, an idea) and never pair with a superlative; “an” additionally only precedes a vowel sound, which “largest” does not have. Leaving the slot empty is also wrong because a singular countable superlative phrase still needs its determiner.