We tend to echo the pattern used in the question:
1. Has the car any gears? - Yes, it has.
2. Has the car got any gears? - Yes, it has.
3.Does the car have any gears? - Yes, it does,
However, there is no obligation for this. Some speakers might respond in different ways.
Incidentally, the 'any' seems a little unnatural to me. Cars normally have gears (however man