Final answer:
The Chagatai Khanate weakened itself in several failed attempts to conquer the Delhi Sultanate.
Step-by-step explanation:
The Mongol Khanate that weakened itself in several failed attempts to conquer the Delhi Sultanate was the Chagatai Khanate. Despite their domestic turmoil and conflicts with neighboring Mongol Khanates, the Chagatai Khanate launched periodic raids against the Delhi Sultanate for plunder. These attempts, spanning from 1296 to 1306, ultimately failed due in part to the capable ruler of the Delhi Sultanate at that time, Alauddin Khilji.