Among the four alternatives, Khizr Khan alone satisfies the full historical condition. Khizr Khan established Sayyid rule in 1414 after Timur's invasion had weakened Delhi; he initially governed without assuming the full royal title of sultan. This problem belongs to the institutional history of the Delhi Sultanate, where authority depended on mobile military elites, revenue assignments and close supervision from the capital. The distractors need separate rejection: Daulat Khan Lodi belongs to a different institution, context or chronology; Mubarak Shah does not perform the function described in the stem; and Bahlul Lodi fails the required association. The wording of “Who founded the Sayyid dynasty after the decline of Tughluq authority in Delhi?” is deliberately specific, so the candidate should isolate its operative clue before recalling names. — Khizr Khan”, but also remember the factual reason stated above.