Step 1: Understanding the Concept:
The question asks to identify a description that is characteristic of the writing style and content of Al-Biruni, a renowned 11th-century Persian scholar who wrote a detailed account of India called \textit{Kitab-ul-Hind}.
Step 2: Detailed Explanation:
Let's analyze the options and associate them with the correct travelers:
(1) Explanation of the caste system by looking for parallels in ancient Persia: This is a hallmark of Al-Biruni's methodology. To explain the Indian varna system to his non-Indian audience, he tried to find analogies, such as the four social classes that were said to have existed in ancient Persia. This comparative and analytical approach is unique to him among medieval travelers.
(2) Description of Delhi and Daulatabad as vast cities: This description is famously from the account of Ibn Battuta, a 14th-century Moroccan traveler who visited India during the reign of Muhammad bin Tughlaq.
(3) Finding the lack of private property in India: The observation that all land in India was owned by the king, leading to a lack of private property among the nobility, is a central theme in the account of François Bernier, a 17th-century French physician at the Mughal court.
(4) Description of the coconut and the paan: Detailed and fascinated descriptions of the coconut (which he compared to a human head) and the betel leaf (\textit{paan}) are prominent in the travelogue of Ibn Battuta.
Step 3: Final Answer:
The explanation of the caste system using parallels from Persia is a distinctive feature of Al-Biruni's account.