Final answer:
The Khanate of the Golden Horde was the only part of the Mongol world in which the rulers did not convert to Islam.
Step-by-step explanation:
The only part of the Mongol world in which the rulers did not convert to Islam was the Khanate of the Golden Horde.
The Mongol Empire fragmented into four parts, and most of the rulers of these parts, including the Il-Khanate and the Chagatai Khanate, eventually converted to Islam. However, the Mongol rulers of the Golden Horde remained non-Islamic, and the lands west of the Volga River, which were predominantly Orthodox Christian, did not see a majority conversion to Islam.
While the Mongol Empire was religiously diverse, with subjects practicing different faiths such as Islam, Christianity, and Buddhism, only the Golden Horde rulers did not convert to Islam.