Which two of the following tasks are carried out by all operating systems?

The tasks every operating system performs are Statement 3 managing system resources including memory and Statement 4 transferring data to the printer, both part of controlling hardware and resources.

Statement 1 repairing the mouse is a physical hardware repair, not something software carries out.

Statement 2 data logging is a specialised application task, not a universal operating system function.

Statement 5 drawing an image is done by application software such as a graphics program, not the operating system itself.

Managing memory means allocating and freeing it among running programs.

Handling input and output devices, including the printer, is a core resource-management duty of an operating system.