The ruler of Travancore who introduced modern education and administrative reforms with British cooperation was:

The correct answer is: Swathi Thirunal.

Swathi Thirunal Rama Varma (1813–1847) was the Maharaja of Travancore from 1829 to 1847. He was a scholar, musician, and composer who introduced modern education and administrative reforms with British cooperation.

Uthram Thirunal Marthanda Varma (1724–1758) was the Maharaja of Travancore from 1729 to 1758. He is considered to be the founder of modern Travancore.

Ayilyam Thirunal Rama Varma (1782–1809) was the Maharaja of Travancore from 1802 to 1809. He is known for his military reforms and for expanding Travancore’s territory.

Visakham Thirunal Rama Varma (1832–1885) was the Maharaja of Travancore from 1880 to 1885. He is known for his administrative reforms and for promoting education in Travancore.

Swathi Thirunal was born in Thiruvananthapuram, Travancore, on 18 October 1813. He was the son of Maharaja Gowri Lakshmi Bayi and Rama Varma Valiya Koil Thampuran. He was educated at the Pazhavangadi Palace School and the Sanskrit College in Thiruvananthapuram. He was also a student of the French scholar and musician, Louis Alexandre de Laborde.

Swathi Thirunal ascended the throne of Travancore on 1 July 1829. He was a progressive ruler who introduced many reforms in Travancore. He established schools, colleges, and hospitals. He also introduced a new system of administration. He was a patron of the arts and literature. He composed many songs and poems in Sanskrit, Malayalam, and Tamil. He was also a musician and played the veena, the mridangam, and the violin.

Swathi Thirunal died on 16 September 1847 at the age of 33. He was succeeded by his son, Ayilyam Thirunal Rama Varma.