Dear Sango,

Lucknow university takes direct admission only when the seats are left vacant after the entrance examination, and mostly seats are left from the courses like B.tech/MCA/MBA only, others seats are already filled by counselling of entrance examination mostly for PG degrees.

So there is very less chance that you will get admission in PHD without entrance exam, now you haven't given the Entrance exam then you can either wait for the next year or in other reputed Universities.

Best of Luck!!!