Consider the following statements.
1. St. Francis Xavier was one of the founding members of the Jesuit Order.
2. St. Francis Xavier died in Goa and a church is dedicated to him there.
3. The Feast of St. Francis Xavier is celebrated in Goa each year.
Which of the statements given above are correct?

The correct option is 1 and 3 only.

Let us analyze each statement step-by-step to understand why this option is correct:

Statement 1: St. Francis Xavier was one of the founding members of the Jesuit Order.
This statement is correct. St. Francis Xavier, along with St. Ignatius of Loyola and five other companions, co-founded the Society of Jesus (Jesuit Order) at Montmartre, Paris, in 1534.

Statement 2: St. Francis Xavier died in Goa and a church is dedicated to him there.
This statement is incorrect. St. Francis Xavier did not die in Goa; he died on Shangchuan Island, China, on December 3, 1552, while waiting for permission to enter mainland China. His mortal remains were later brought to Goa and are kept in the Basilica of Bom Jesus, which is dedicated to him.

Statement 3: The Feast of St. Francis Xavier is celebrated in Goa each year.
This statement is correct. The Feast of St. Francis Xavier is celebrated every year on December 3rd in Goa (at the Basilica of Bom Jesus in Old Goa) to mark the anniversary of his death.

Therefore, only statements 1 and 3 are correct, making 1 and 3 only the right answer.