The correct answer is option 1 - 1, 2 and 3.

Option 1 states that the presence of the Mughals in the south was not as strong as it was in the north. This meant that there was less competition for European trading companies, allowing them to establish a stronger presence in the region.

Option 2 mentions that the Vijaya Nagar kingdom had been overthrown in the late 16th century. This event weakened the local power structure in South India, making it easier for European trading companies to establish their dominance.

Option 3 states that the south had many small and weak states. This fragmentation of power made it easier for European trading companies to negotiate and establish favorable trading agreements with these states.

Therefore, all three reasons mentioned in the options contributed to the success of European trading companies in South India during the 17th century. These factors provided favorable conditions for the expansion and establishment of European trade in the region.