Ja, u kunt dit doen door de rijen op te sommen en vervolgens de top drie op te halen:
select r.id, r.question, r.category
from (select r.*,
(@rn := if(@c = category, @rn + 1,
if(@c := category, 1, 1)
)
) as seqnum
from `random` r cross join
(select @rn := 0, @c := -1) params
order by category, rand()
) r
where seqnum <= 3;