I've got a dump from my Drupal database that I've created with Backup and Migrate.
I want to find out which versions of the modules ctools and Panels have been in use.
Where do I have to look? What do I have to search for?
Run below query
filename LIKE '%ctools.module%'
LIMIT 0 , 30
You will see version information in info column. Search for "Version". Above information is serialized.
For Example, As you see below "Ctools" module is 6.x-1.11 version. You can do same for panels module by changing query.
Aside from database dump, with the "Views System" module you can get details (although it seems a bit unstable).