Can you run a full database backup and a file shrink at the same time?
Can you run a full database backup and a filegroup backup at the same time?
Answer to both of the questions are NO.
Can you run run full back and log backup at the same time?
Answer is Yes
How to you know these? What can be done with what? Here is the chart which tells you about it?
This image will tell you the story.
Not all administrative tasks are allowed to run concurrently. In the table above, a black circle indicates two operations that cannot run in a database at the same time.