BIOS is probably the best option. BIOS is fixed to the motherboard and cannot be swapped between other boards. That would constitute a component "of" the motherboard. The CPU is its own thing on a similar footing as the motherboard itself. I would hesitate to call it a part of the motherboard, considering it doesn't come with the motherboard.
Transistors are fundamental elements of processors. If they were to be a component "of" something, it would be the processor, not the motherboard.
I think Bios is a better answer than a processor. Although both incorrect for this question. Transistor should be the correct answer, as most transistors these days are found embedded into circuits. Processor is not a component of the larger whole in this case (as we're looking for a component, or part of the motherboard, not something attached.) And the BIOS is again, attached not necessarily integrated. (although, when improper flashing of a bios is done, you might as well just go out and buy a new motherboard as finding a replacement bios can be more of a pain than finding a replacement processor.)