Yes, you could store the questions using CoreData and read them from a JSON file or similar when the app starts. This will allow you to update the questions via a REST api
If you would use a DB I'd suggest to organize the questions in this way so it would be simple to use a single view and access the questions with SQL.
Code:
Q Table
QID | Q | Answer | Category
1 | What is the capital of France? | Paris | geo
2 | What is 7 + 2 | 5 | math
I suggest also to check this source code, it could be useful if you are not so confident in developing:
http://www.chupamobile.com/products/details/628/Quiz+Maker+Starter+Kit/