Statement 1 is incorrect. The first significant Mongol invasion of India occurred during the reign of Iltutmish when Jalal-ud-din Mangburni of Khwarazm sought refuge in India, leading to Mongol forces under Genghis Khan appearing on the Indus. The Khalji dynasty came later. Statement 2 is correct. During the reign of Ala-ud-din Khalji, the Delhi Sultanate faced multiple Mongol invasions. A notable invasion led by Targhi in 1303 reached the gates of Delhi and besieged the city, forcing Ala-ud- din to take refuge in the Siri fort. Statement 3 is incorrect. While Muhammad-bin-Tughlaq did face Mongol invasions (e.g., by Tarmashirin), historical accounts suggest he often adopted policies like paying tribute or using diplomacy to repel them, rather than permanently losing significant portions of his core kingdom in the north-west to the Mongols as a result of these invasions. Control over frontier regions was often contested, but a sustained loss of territory to the Mongols during his reign is not a commonly accepted historical fact in the way implied by the statement.