IBPS SO Prelims Exam Model Paper 5

The correct answer is Option 4).
Statement 1) His ordinary life was that of an officer of the Guards, modified by the ceremonial duties incumbent on him as heir to the throne.
In this sentence incumbent means necessary for (someone) as a duty or responsibility. As the person being heir to the throne has some ceremonial duties to perform.
Statement 2) At the East end of the church is an incumbent statue of Mary Magdalene with her pot of precious ointment by her side.
Here the word 'incumbent' makes no sense. 'a recumbent' should be there in place of 'an incumbent'. Recumbent means (especially of a person or effigy) lying down. There was a lying statue of May Magdale at the East end of the church.
Sentence 3) An incumbent, once inducted, can only be disturbed by complicated and extremely costly processes of law.
Here incumbent means the holder of an office or post.
So clearly the correct answer is Option 4).