Ghenghis Khan invaded India during the reign of which of the following?

Iltutmish

The correct answer is Option 2- Iltutmish

The Mongol Empire during 1221-1327 came up with many invasions in the Indian subcontinent with many of the later raids were made by the unruly Qaraunas of Mongol origin. it was during the reign of Iltutmish that the Mongols under Genghis Khan invaded India.

Ghenghis Khan's forces did not directly conquer a significant part of India  during his reign.
Genghis Khan sent military detachments led by generals like Dorbei and Bala to pursue the fleeing Khwarizm Shah (ruler of the Khwarazmian Empire) who had sought refuge in the Indus Valley.
These Mongol forces raided some areas in the western part of the Delhi Sultanate, particularly around the Indus River and the region of Punjab.
Iltutmish was the Sultan of Delhi during this time. He refused to offer asylum to the Khwarizm Shah, potentially preventing a full-fledged Mongol invasion.
The Mongol invasions of India occurred later, after Genghis Khan's death, during the reign of his descendants.