I bought this 98 GS500E 3mounth back and this is my first one. Initially after 400mi the engine was back firing with the sparkplugs black in color. I cleaned the carbs and was running fine but after 500mi the problem has again started. can any one suggest what may be the prob.

Too much fuel methinks. Running very rich.

i cleaned the carbs and adjusted the jets but still its running rich

Adjust the jets and rich ... prolly not ... unless your floats are super super high ... then it will run fine at bigger throttle openings and misfire and die at low revs.
Cool.
Srinath.

Is your MPG really bad? if you're getting under 50 you are probally too rich, check for clogged air filter. Also when your carbs were apart did you notice the jet sizes? stock should be 37.5 pilot and 122.5 main, if they are much richer than that without a pipe and filter, that could foul plugs. Excessive oil consumption could do that too, but you'd have to be going through some serious oil and blowing some pretty nasty smoke. blue smoke=oil black smoke=too much gas