Consider the following statements.
1. It was during the reign of Iltutmish that Chengiz Khan reached the Indus in pursuit of the fugitive Khwarezm prince.
2. It was during the reign of Muhammad bin Tughluq that Taimur occupied Multan and crossed the Indus.
3. It was during the reign of Deva Raya II of Vijayanagara Empire that Vasco da Gama reached the coast of Kerala.
Which of the statements given above is/are correct?

The correct option is 1 only.

Let us analyze each statement individually to determine its correctness:

Statement 1: It was during the reign of Iltutmish that Chengiz Khan reached the Indus in pursuit of the fugitive Khwarezm prince.
• During the reign of Shams-ud-din Iltutmish (1211–1236 CE), the Mongol leader Chengiz Khan invaded Central Asia.
• Jalal-ud-din Mangabarni, the Shah/prince of Khwarezm, fled towards India after being defeated by Chengiz Khan.
• Chengiz Khan pursued him up to the banks of the River Indus in 1221 CE.
• When Jalal-ud-din requested asylum from Iltutmish, Iltutmish diplomatically refused, saving the infant Delhi Sultanate from the wrath of Chengiz Khan.
• Hence, Statement 1 is correct.

Statement 2: It was during the reign of Muhammad bin Tughluq that Taimur occupied Multan and crossed the Indus.
• Timur (Taimur) invaded India in 1398 CE.
• At that time, the ruler of the Delhi Sultanate was Sultan Nasir-ud-din Mahmud Shah Tughluq (the last ruler of the Tughluq dynasty, who reigned from 1394 to 1412 CE), not Muhammad bin Tughluq (who reigned much earlier, from 1325 to 1351 CE).
• Hence, Statement 2 is incorrect.

Statement 3: It was during the reign of Deva Raya II of Vijayanagara Empire that Vasco da Gama reached the coast of Kerala.
• Vasco da Gama reached Calicut (Kozhikode) on the coast of Kerala in 1498 CE.
• Deva Raya II ruled the Vijayanagara Empire from 1424 to 1446 CE.
• In 1498 CE, the ruler of the Vijayanagara Empire belonged to the Saluva dynasty (Immadi Narasimha Raya under regent Tuluva Narasa Nayaka).
• Hence, Statement 3 is incorrect.

Therefore, only statement 1 is correct.