Hello Arun,
As you have scored 68.6% with Maths stream it is not a bad score.Now if you want to know about the procedure of admission in different government colleges.Actually it depends on,in which field you want to continue your further studies.If you want to do engineering with this percentage you can get only private colleges if you want but if you have applied for JEE MAINS you can apply for government college also, and you should apply for them. If you want to do any simple degree for graduation you can get goverment college for that. You can apply for that whatever in which you are interested.So overall it depends on your interest in the hich field you want to go.