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The given question provides three pairs of eminent persons and their well-known fields. We need to determine which pair is correctly matched.
1. Amartya Sen - Economist: This pair is correctly matched. Amartya Sen is a renowned economist who has made significant contributions to the field of welfare economics and development economics.
2. Kapila Vatsyayan - Sculptor: This pair is not correctly matched. Kapila Vatsyayan is not known as a sculptor. She is a notable Indian scholar, dancer, and art historian.
3. Hari Prasad Chaurasia - Novelist: This pair is also not correctly matched. Hari Prasad Chaurasia is not known as a novelist. He is a renowned flutist and Indian classical musician.
So, only pair 1 (Amartya Sen - Economist) is correctly matched. Therefore, the correct answer is option 1 - 1 only.