Hello student!
You can definitely go for btech without giving your jee examination.this is called direct admission in the college.Some colleges have a basic criteria for jee mains score but many colleges take direct admission on the basis of the score in the test that they themselves take when youll go to them for the admission.except iits and niits you can go for direct admission . And there are a number of colleges in India you have ample of options to you for direct admission too.

Hope this helps you!
Regards!