I am preparing for competitive exams and for this am trying my best to qualify in teacher exam. I need to work more harder to clear this exam. I don't know how to manage salah, reciting quran and namaz e shab. I can't skip salah for this. Can you please guide me how to manage studies and ibadat and am requesting you to kindly let me know some duas to help me in this exams

The quantity of prayers does not matter. Quality matters. It is enough that you concentrate on the wajib prayers to perform them in the right way, and if your time is too busy, at least spare few minutes for night prayer (minimum 3 raka'ats of shaf'a and witir, before you go to sleep.
On the other hand, I advise you to sit for a while and re arrange your time, and you will find gaps here and there for reading quran as well.
Wish you all the best.