Can i directly give my t.y.ba bachelor of arts exam after 12th?

No, you cannot directly give a T.Y. BA (Third Year Bachelor of Arts) exam after 12th standard. T.Y. BA is the *third* year of a three-year Bachelor of Arts degree. You must first complete the first two years (F.Y. BA and S.Y. BA) before you can attempt the final year (T.Y. BA) exams.