The correct option is Option 2: Fruits and palm oil.

Arid and semi-arid countries in the Middle East face challenges in agricultural production due to their dry climate and limited water resources. As a result, they often rely on importing food and agricultural products from other countries, including India. Here`s a detailed reasoning for choosing Option 2:

1. Raw wool and carpets (Option 1): Arid and semi-arid countries in the Middle East are not known for significant wool production. These countries typically have a desert-like climate, which is not suitable for sheep farming or wool production on a large scale. Therefore, it is unlikely that they would export raw wool and carpets to India.

2. Precious stones and pearls (Option 3): While the Middle East is known for its production and trade of precious stones and pearls, particularly countries like Saudi Arabia and the United Arab Emirates, these commodities are not directly linked to the arid and semi-arid nature of these countries. Precious stones and pearls can be found in various regions globally, and their export to India is not specific to arid or semi-arid countries in the Middle East.

3. Perfume and coffee (Option 4): The production and export of perfume and coffee are not strongly associated with arid and semi-arid countries in the Middle East. Perfume production is more commonly linked to countries like France and Italy, known for their fragrance industry. Similarly, coffee production is concentrated in countries like Brazil, Vietnam, and Colombia, rather than arid or semi-arid regions.

4. Fruits and palm oil (Option 2): Arid and semi-arid countries in the Middle East, such as Saudi Arabia, the United Arab Emirates, and Qatar, heavily rely on imports for their food needs due to limited agricultural capabilities. India, being a significant agricultural producer, is a potential source of fruits and palm oil for these countries. Fruits are a vital part of the diet and can be imported from countries like India, which has a diverse range of fruits available for export. Additionally, palm oil is an essential cooking oil and is commonly used in various food products. India is one of the largest importers of palm oil globally, and arid and semi-arid countries in the Middle East can export palm oil to India to meet its demand.

In conclusion, Option 2 (Fruits and palm oil) is the most likely set of commodities that arid and semi-arid countries in the Middle East would export to India, given the climatic conditions and the import requirements of these countries.