How to find out what profile was used for building *.ipa file?

I can give you a direction in this, not sure if it’ll actually help:

1. Change the extension of the *.ipa file to *.zip.
2. Un-archive this zip file.
3. The folder contains a *.app file. Open its package contents by right clicking it.
4. Inside, you’ll find an embedded.mobileprovision file.

EDIT- Since Xcode 6 doesn’t show the provisioning profile, I’ll extend the answer to still see the details:

5. Change the extension of the embedded.mobileprovision to embedded.txt or just open it with any text editor of choice.
6. Inside, you’ll find some binary data and a hash that contains the profile’s details like Entitlements, CreationDate, ExpirationDate, Name, etc which will be sufficient to conclusively lead you to the provisioning profile used to create the .ipa.

Hope it’ll help!