The official language in the court of the Mughals in Medieval India was Persian (option 1). Persian was widely used as the language of administration, law, and diplomacy during the Mughal Empire. It was the preferred language of the Mughal emperors and the elite class. Persian was chosen for its prestige and because it was the language of the Persianate culture that influenced the Mughal Empire.

Option 2, Pushtu, is incorrect. While Pushtu is a regional language spoken in parts of present-day Afghanistan and Pakistan, it was not the official language of the Mughal court.

Option 3, Arabic, is also incorrect. While Arabic is an important language in Islam and was used in religious contexts, it was not the official language of the Mughal court.

Option 4, Urdu, is incorrect as well. Urdu evolved from the interaction between Persian and the languages spoken in northern India. It became widespread during the later Mughal period and eventually became the language of the royal court in the 18th century, during the decline of the Mughal Empire.

In summary, the correct answer is option 1, Persian, as it was the official language in the court of the Mughals