The term "brain of the computer" refers to the component that actually carries out instructions, performs calculations, and makes logical decisions, since this is the role the human brain plays in the body.
The Central Processing Unit is the component that fetches program instructions, decodes them, and executes them, coordinating every other part of the computer while doing so. It contains the arithmetic and logic unit, which performs calculations and comparisons, and the control unit, which directs the flow of data between memory and other devices. Without it, no processing of any kind could take place.
A monitor only displays output, a mouse only sends positional input signals, and a printer only produces output on paper; none of these devices process or interpret data. They depend entirely on the processing done elsewhere to have anything meaningful to display or print.
Examination reminder: when a question asks which component performs processing and decision-making, the answer always points to the Central Processing Unit, not to input or output peripherals.