The correct answer is A. Ghiyasuddin Tughlaq.
Ghiyasuddin Tughlaq was the founder of the Tughlaq dynasty, which ruled the Delhi Sultanate from 1320 to 1388. He was born in 1260 in Turkistan and came to India in 1296. He served as a general under Alauddin Khalji and played a key role in the conquest of Gujarat. In 1320, he ascended the throne of Delhi after the death of Alauddin Khalji’s son, Mubarak Shah.
Ghiyasuddin Tughlaq was a capable ruler and expanded the territory of the Delhi Sultanate. He built new cities, including Tughlaqabad and Firozabad. He also introduced a number of reforms, including the introduction of a new currency and the construction of a new irrigation system.
Ghiyasuddin Tughlaq died in 1325. He was succeeded by his son, Muhammad bin Tughluq.
Option B, Muhammad Shah Tughlaq, was the third Sultan of the Tughlaq dynasty. He ruled from 1325 to 1351. He was the son of Ghiyasuddin Tughlaq.
Option C, Ferozshah Tughlaq, was the fifth Sultan of the Tughlaq dynasty. He ruled from 1351 to 1388. He was the son of Muhammad bin Tughluq.
Option D, Nasiruddin Mahmud, was the sixth Sultan of the Tughlaq dynasty. He ruled from 1388 to 1390. He was the son of Ferozshah Tughlaq.