The correct answer is option 3, which states that all the given characteristics about the state of Travancore in 18th century Kerala are correct. Let`s analyze each option to understand why this is the correct answer.
Option 1 states that Travancore was ruled by Marthanda Varma from 1729 to 1758. This is correct, as Marthanda Varma was the ruler of Travancore during this period and is known for his contribution to the state`s development.
Option 2 states that Travancore built a strong army and defeated the Dutch in 1741. This is also correct. Marthanda Varma successfully built a powerful army and defeated the Dutch East India Company in the Battle of Colachel in 1741, establishing Travancore`s military prowess.
Option 3 states that Travancore was an important center of learning. This statement is correct as well. Travancore had a thriving intellectual and cultural environment, with institutions like the Royal College of Thiruvananthapuram promoting education and knowledge.
Therefore, based on the given information, all the characteristics about the state of Travancore in the 18th century are correct, making option 3 the correct answer.