The vacancy was filled (1)/ by a young scholar (2)/ who had an extensible knowledge of ancient art. (3)/ No error. (4)

Answer

3

Explanation

extensive will replace extensible extensible (Adj.) : capable of being extended extensive (Adj.) : thorough, dealingwitha widerange of information
Look at the examples given below:
We had fairly extensive discussions.
These tables are extensible.
Hence, who hadanextensive knowledge ofancient art is the right usage.