The correct statement is 2 only, as during the reign of Ala-ud-din Khalji, the Mongols did launch a significant assault that led to the siege of Delhi in 1299-1300. This event highlights the persistent threat posed by the Mongols to Indian territories during this period, illustrating the geopolitical challenges faced by Indian rulers. Statements 1 and 3 are inaccurate; the first Mongol invasion occurred under the rule of Iltutmish, and the loss of territories in the northwest under Muhammad-bin-Tughlaq was primarily due to regional instability and not directly attributed to a Mongol invasion. Understanding these events is crucial for analyzing the historical dynamics of power and resistance in medieval India, particularly in relation to foreign invasions.