Match List-I with List-II:

$$\begin{gathered} \mathrm{List-I} \\ \text{ Incident / Characteristics} \end{gathered}$$	$$\begin{gathered} \mathrm{List-II} \\ \text{ Traveller} \end{gathered}$$
$\left(A\right)\text{He arrived in Ghazni as a hostage, but gradually developed a liking for this city}$	$\left(I\right)\text{Al-Biruni}$
$\left(B\right)\text{He reached Sind in 1333 and was later appointed as the qazi of Delhi}$	$\left(\mathrm{II}\right)\text{François Bernier}$
$\left(C\right)\text{Physician to Prince Dara Shukoh}$	$\left(\mathrm{III}\right)\text{Ibn Battuta}$
$\left(D\right)\text{Wrote a detailed account of trade and society in South India}$	$\left(\mathrm{IV}\right)\text{Duarte Barbosa}$

Choose the correct answer from the options given below:

The correct answer is (A)- (I), (B)- (III), (C)- (II), (D)- (IV).

Let us break down the logical matching between the incidents/characteristics in List-I and the respective travellers in List-II step-by-step:

1. Matching (A):
Incident/Characteristic: "He arrived in Ghazni as a hostage, but gradually developed a liking for this city"
Explanation: Al-Biruni was born in Khwarazm (modern-day Uzbekistan). In 1017, when Sultan Mahmud of Ghazni invaded Khwarazm, he took several scholars and poets back to his capital, Ghazni, as hostages or captives. Al-Biruni was among them. Although he arrived as a hostage, he spent the rest of his life in Ghazni, developed a deep liking for the city, and wrote his famous work Kitab-ul-Hind there.
Therefore, (A) matches with (I) Al-Biruni.

2. Matching (B):
Incident/Characteristic: "He reached Sind in 1333 and was later appointed as the qazi of Delhi"
Explanation: Ibn Battuta, the Moroccan traveller, reached the Sindh region of the Indian subcontinent in the year 1333. He went to Delhi, where Sultan Muhammad bin Tughlaq, impressed by his scholarship and expertise in Islamic law, appointed him as the qazi (judge) of Delhi.
Therefore, (B) matches with (III) Ibn Battuta.

3. Matching (C):
Incident/Characteristic: "Physician to Prince Dara Shukoh"
Explanation: François Bernier was a French physician and traveller who arrived in India during the Mughal empire. He was associated with the Mughal court and served as a personal physician to Prince Dara Shukoh, the eldest son of Emperor Shah Jahan.
Therefore, (C) matches with (II) François Bernier.

4. Matching (D):
Incident/Characteristic: "Wrote a detailed account of trade and society in South India"
Explanation: Duarte Barbosa was a Portuguese writer and officer who travelled in India in the early 16th century. He wrote a detailed travelogue covering trade, customs, and society in southern India, particularly focusing on the Vijayanagara Empire and the Malabar coast.
Therefore, (D) matches with (IV) Duarte Barbosa.

Combining all the individual matches, we get:
(A) → (I), (B) → (III), (C) → (II), (D) → (IV), which corresponds to the second option.