Can an adapter like the one in the photo be used to connect a keyboard and a mouse to a motherboard that only has at connector like some socket 7 and 486?
no
edit: such a cable also won't work on the majority of mainboards which actually use a ps2 connector.
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https://www.vogonswiki.com/index.php/Serial_port
Indeed, and the most visible reason is that the PC/XT/AT keyboard connector is only 5 pins, while 2-in-1 PS/2 connectors use all 6 (common power/ground, 2 clocks and 2 data lines) 😀
[On those, there's also no standard on which is the main device, so if you get a competing brand splitter you may need to connect the keyboard to the green socket, etc]
