It's certainly possible to write such an exam, perhaps even put it into some HTML or even CGI format to check results and mail them somewhere, or just something that prints out well.

If such a thing already exists on line, such as 'brainbench.com' it's probably going to cost some money to take it. Who's going pay?

Any of the monks here could probably write a half decent test in probably under an hour, and then spend the next two weeks debating the merits of various questions.