Correct Option
Statement 1 is correct. During the reign of Iltutmish (1211–1236 CE), the Mongol leader Chengiz Khan reached the Indus River in pursuit of Jalaluddin Mangbarani, the fugitive Khwarezmian Prince. Iltutmish prudently refused asylum to Jalaluddin, thereby preventing a direct Mongol invasion of the Delhi Sultanate.
Incorrect Options
Statement 2 is incorrect. Taimur (Timur) invaded India in 1398 CE. At this time, the Delhi Sultanate was ruled by Nasiruddin Mahmud Tughlaq, not Muhammad bin Tughlaq, whose reign was from 1325–1351 CE. Taimur's invasion resulted in the plunder of Delhi and significantly weakened the Tughlaq dynasty.
Statement 3 is incorrect. Vasco da Gama arrived on the coast of Kerala (Calicut) in 1498 CE. Deva Raya II, a prominent ruler of the Vijayanagara Empire, reigned from 1425 to 1446 CE. Therefore, Deva Raya II was not the contemporary ruler when Vasco da Gama reached India. The local ruler of Calicut at the time was the Zamorin.