Background:
During the reign of the Delhi Sultanate, foreign visitors played significant roles in various aspects of administration, including the judiciary. One such visitor was Ibn Batuta, who was appointed as the Qazi of Delhi by the reigning monarch.

Explanation:
Ibn Batuta, also known as Abu Abdullah Muhammad Ibn Abdullah Al Lawati Al Tanji Ibn Batuta, was a famous Moroccan scholar, explorer, and traveler who visited India during the 14th century. He was appointed as the Qazi of Delhi by the then reigning monarch, Muhammad bin Tughluq.

Who were the other options?
a) Abdur Razzaq: Abdur Razzaq was a Persian ambassador who visited India during the reign of Sultan Mahmud Tughlaq. However, there is no historical evidence to suggest that he was appointed as the Qazi of Delhi.

c) Zamil Beg: Zamil Beg is not a known historical figure, and there is no record of his visit to India or appointment as the Qazi of Delhi.

d) Vadgar Ali: Vadgar Ali is not a known historical figure, and there is no record of his visit to India or appointment as the Qazi of Delhi.

Why was Ibn Batuta appointed as Qazi of Delhi?
Ibn Batuta was appointed as the Qazi of Delhi due to his extensive knowledge of Islamic jurisprudence and his reputation as a learned scholar. The Sultan, Muhammad bin Tughluq, recognized Ibn Batuta's expertise and appointed him to this prestigious position.

What is the significance of Ibn Batuta's appointment?
Ibn Batuta's appointment as the Qazi of Delhi highlights the cosmopolitan nature of the Delhi Sultanate and its openness to foreign scholars and administrators. It also demonstrates the Sultan's recognition of Ibn Batuta's qualifications and his willingness to entrust him with an important role in the administration.

Conclusion:
In conclusion, among the given options, Ibn Batuta was the foreign visitor appointed as the Qazi of Delhi by the reigning monarch, Muhammad bin Tughluq. His appointment highlights the Sultanate's openness to foreign scholars and administrators, and his expertise in Islamic jurisprudence made him suitable for this prestigious position.