I’m not sure I understand your question, but yes, the Mongols did invade India several times. For a good essay on why they did not succeed in conquering it see here: http://www.mongolianculture.com/MONGOL-ARMIES.htm

The short answer is that Northwest India (the direction from which they launched their various incursions into India) appears to be unsuited for the logistical needs of an all-cavalry army.