Where doIi check provisional state rankings ? What will be my domicile state? Place of birth or place where i completed 10th and 12th ?

Each state council will release the provisional stat rankings and they shall be available online.
Karnataka and few other states have already released.

For knowing more about domicile you should visit the state regional office as enquire about the criteria of doniiile. Each state has a different and respective criteria for giving domicile.