Step 1: Understand the Task
The objective is to match prominent foreign travelers to medieval India with significant events or characteristics from their lives and writings.
Step 2: Detailed Matching
(A) Taken hostage to Ghazni: In 1017, when his homeland Khwarizm fell to Mahmud of Ghazni, (I) Al-Biruni was captured and brought to Ghazni. This experience sparked his interest in India, leading him to accompany Mahmud's expeditions.
(B) Arrived in Sind and appointed Qazi of Delhi: The Moroccan traveler (III) Ibn Battuta landed in Sind in 1333. In Delhi, Sultan Muhammad bin Tughlaq, impressed by his intellect, appointed him as the *qazi* (judge).
(C) Physician to Prince Dara Shukoh: The French traveler (II) François Bernier arrived in India in the mid-17th century. He served for several years as a physician to Dara Shukoh, the eldest son of Emperor Shah Jahan.
(D) Documented South Indian trade and society: The Portuguese writer and official (IV) Duarte Barbosa traveled to India in the early 16th century. He meticulously recorded the trade, social norms, and political structures of South India, including a notable account of the Vijayanagara Empire.
Step 3: Final Result
The correct pairings are: A-I, B-III, C-II, and D-IV. This corresponds to option (2).