The source-backed, question-specific record explains: The victory over Prithviraj III enabled Ghurid commanders to extend authority into the Delhi-Ajmer region. Qutb-ud-din Aibak later established an independent Delhi-based sultanate after Muhammad of Ghor’s death in 1206. Tarain was therefore a major enabling conquest, but it did not itself establish the Mamluk or Slave dynasty in 1192. This evidence establishes the historical relationship required in this Important Battles item. A correct solution must preserve the exact battle, date, participants, commander, location, outcome or significance requested by the stem. Similar periods, genres or national traditions do not make two battle facts interchangeable. Option A gives Expansion of Ghurid power into the Delhi-Ajmer region and satisfies every condition stated in the question. The remaining choices—Formal creation of the Mughal Empire, Foundation of the Khalji dynasty and Annexation of Vijayanagara—do not satisfy the complete requirement. Depending on the stem, a distractor may name a real commander but attach the wrong title, use a related event involving another power, reverse a correct association, or present a correct statement when the question specifically asks for the incorrect match. The reliable checking method is to identify the named battle first, recall or verify its verified participant or outcome, and then read qualifiers such as “both works,” “original language,” “first published,” “correctly matched” or “incorrectly matched.” These qualifiers determine what counts as the answer. Replaying that method for this Important Battles question confirms Expansion of Ghurid power into the Delhi-Ajmer region without relying on option position.