The area in India that produces the largest amount of cotton is Option 3: Western and Southern India.

Western and Southern India are known as the major cotton-growing regions of the country. These regions have favorable agro-climatic conditions, including suitable soil types, temperature, rainfall, and availability of irrigation facilities, which are essential for cotton cultivation. Let`s explore each of these regions in detail:

1. Western India:

Western India comprises states like Gujarat and Maharashtra, which are prominent cotton-growing regions. Gujarat, especially the districts of Surendranagar, Rajkot, and Amreli, is known for its high-quality cotton production. Ahmedabad is one of the largest cotton trading markets in India. The region benefits from the warm and dry climate, black soil, and availability of water from rivers like Sabarmati and Narmada, making it ideal for cotton cultivation.

2. Southern India:

Southern India, particularly the states of Telangana, Andhra Pradesh, Karnataka, and Tamil Nadu, is also a significant cotton-producing area. Telangana and Andhra Pradesh, in particular, are major contributors to India`s cotton production. The region has a tropical climate and fertile alluvial soil, which is suitable for cotton cultivation. Additionally, the Krishna and Godavari river basins provide ample water for irrigation, further supporting cotton farming.

It is important to note that the other options mentioned in the question also have cotton cultivation, but the largest amount of cotton is produced in Western and Southern India.

1. Option 1: North-western India and Gangetic West Bengal:

While North-western India, including Punjab and Haryana, cultivates cotton, the production volume is not as significant as in Western and Southern India. Gangetic West Bengal, on the other hand, is known for jute cultivation rather than cotton.

2. Option 2: North-western and Western India:

As mentioned earlier, Western India, including Gujarat and Maharashtra, is a major cotton-producing region. However, North-western India alone does not produce the largest amount of cotton.

3. Option 4: Plains of Northern India:

The plains of Northern India, including regions like Punjab and Haryana, do cultivate cotton, but their production volume is comparatively smaller than that of Western and Southern India.

In conclusion, when considering the largest amount of cotton production in India, Option 3: Western and Southern India stands out due to their favorable climatic conditions, availability of irrigation facilities, and the presence of significant cotton-growing states like Gujarat, Maharashtra, Telangana, and Andhra Pradesh.