Navigate to the course with the category of questions you wish to export, and click 'More' from the top ribbon

Click the drop down list at the top of the page

Select a format for the export file. In this scenario, Aiken format was selected

If the category you wish to import is not listed, click on the drop down list 

Once the list appears, select the category of questions you wish to export

Click "Export questions to file". Your browser will automatically start downloading the file and it will be accessible from your computer's 'Downloads' folder

Exporting Quiz Questions by Category