The syllabus for entrance exam for Btech is generally from 11th and 12th protions with some exams like jee advance putting few questions based on out of current CBSE syllabus topics, you will be needed to check there exam syllabus online.There are seperate pattern for different exam for different colleges. For example JEE Mains- 360 marks(p-120, c - 120, m - 120), KCET(p -60, c- 60, m- 60) and jee advance pattern is not fixed.

There is no extra syllabus other than your intermediate (+2) syllabus. The entrance test is JEE mains which is of 360 marks (physics-120, chemistry-120, mathematics-120). 80-85 % of questions are from NCERT text book syllabus only. And some other questions are from advanced topics.

Physics is important for so many Engineering branches like Electrical, Mechanical, Electronics, Civil, etc......