To increase the size of the Database Buffer Cache without impacting user connections, you must have started the database instance with a server parameter file (SPFILE).
Explanation for the options:
A) Starting the database instance in restricted mode is not necessary for increasing the size of the Database Buffer Cache. Restricted mode is typically used for performing maintenance activities or troubleshooting specific issues.
B) Starting the database instance in NORMAL mode is not the correct option because it does not specify the use of a server parameter file (SPFILE), which is required to make changes to the memory structures.
C) This is the correct option. Starting the database instance with a server parameter file allows you to make changes to memory structures dynamically, including increasing the size of the Database Buffer Cache.
D) Starting the database instance without mounting it would not allow you to make changes to the memory structures.
E) Starting the database instance but not opening it would not allow you to make changes to the memory structures.
Therefore, the correct answer is C) You must have started the database instance with a server parameter file.