Aeronautical Engineering is one of the branches of aerospace engineering, which deals with the designing and construction of aircrafts that are operated within the atmosphere of the earth.

As you are looking for the date of the Aeronautical Engineering Entrance Exams but you have not mention the name of exam, I have dates of following Aeronautical Engineering Entrance Exams so please let me know for which you are looking

Graduate Level Aeronautical Engineering Entrance Examinations in India

C.E.E or Combined Entrance Examination of D.U or University of Delhi
Indian Institute of Aeronautics (I.I.A) Entrance Exam
J.E.E or Joint Entrance Exam of I.I.T or Indian Institute of Technology
S.E.T or S.L.I.E.T Entrance Test
S.R.M.E.E.E or S.R.M Engineering Entrance Examination
H.I.T.S.E.E or Hindustan Institute of Technology and Science Entrance Test
I.I.S.A.T Admission Test of I.I.S.T of Thiruvananthapuram

Postgraduate Level Aeronautical Engineering Entrance Examinations in India

G. A. T. E. or Graduate Aptitude Test in Engineering
Sathyabama University M. E. Entrance Examination
Punjab Engineering College Ph. D Entrance Examination