why bluetooth is not operated at low frequency, since low frequency has large wavelenth ,can travel more distance and power requirement will also be low .

 

You need a larger antenna for a larger wavelength. Do you want a 15 foot antenna hanging off your ear?

 

Why not modulate the lower frequency signal onto the higher frequency signal? This question applies to all communications. Hi frequency requires line of sight, but low frequency bounces off the ionosphere. Why not take advantage of the latter in any case that is practical?