Iltutmish was the ruler of the Delhi Sultanate from 1211 to 1236. During his reign, the Mongols under Genghis Khan did not invade India. The correct answer to the question should be option 'D', Muhammad bin Tughlaq.

Explanation:
I. Mongol Invasions in India:
- The Mongols, led by Genghis Khan, were known for their large-scale invasions and conquests. They had already established a vast empire extending from Asia to Europe.
- During the 13th century, the Mongols launched several invasions into the Indian subcontinent, aiming to expand their empire further.
- These invasions were part of the larger Mongol conquests that aimed to establish a hegemony over the entire known world.

II. Rulers during Mongol Invasions:
a) Balban:
- Ghiyas ud-Din Balban was the ninth ruler of the Delhi Sultanate, reigning from 1266 to 1287.
- He faced numerous challenges during his rule, including Mongol incursions, but he successfully repelled those invasions.

b) Feroz Tughlaq:
- Feroz Shah Tughlaq was the Sultan of Delhi from 1351 to 1388.
- Although his reign witnessed several conflicts and rebellions, there were no major Mongol invasions during his time.

c) Iltutmish:
- Iltutmish was the third Sultan of Delhi, ruling from 1211 to 1236.
- He successfully defended the Delhi Sultanate against the Mongols, led by Genghis Khan's successors.
- Iltutmish's strong military leadership and strategic alliances allowed him to repel the Mongol invasions during his reign.

d) Muhammad bin Tughlaq:
- Muhammad bin Tughlaq was the Sultan of Delhi from 1325 to 1351.
- His reign witnessed the Mongol invasions into India.
- In 1327, the Mongols, under the leadership of Tarmashirin Khan, invaded the Punjab region and sacked the city of Lahore.
- Muhammad bin Tughlaq struggled to counter the Mongol threat, and the invasions caused significant devastation in northern India.

In conclusion, the correct answer to the question is option 'D', Muhammad bin Tughlaq. It was during his reign that the Mongols invaded India, while Iltutmish successfully defended the Delhi Sultanate against them.