The correct option is option 1, Khizr Khan. He was the founder of the Sayyid Dynasty in the Delhi Sultanate. The Sayyid Dynasty ruled from 1414 to 1451, which was the last dynasty of the sultanate. Khizr Khan was a prominent noble and military commander who served under the Tughlaq dynasty. He established the Sayyid Dynasty after overthrowing the Tughlaq dynasty and taking power in Delhi.

Option 2, Mubarak Shah, is incorrect. Mubarak Shah was a ruler of the Tughlaq dynasty and not the founder of the Sayyid Dynasty.

Option 3, Muhammad Shah, is also incorrect. There is no historical evidence of a ruler by this name being associated with the Sayyid Dynasty.

Option 4, Alauddin Alam Shah, is also incorrect. Alauddin Alam Shah belonged to the Sayyid Dynasty but he was not the founder. He ruled after Khizr Khan and was his successor.

In conclusion, the founder of the Sayyid Dynasty in the Delhi Sultanate was Khizr Khan, and he established the dynasty after overthrowing the Tughlaq dynasty.