Hello,
there is exam and screening test for every thing after 10th. even small childs give exam to join school.
for every new thing you join there will be sure an exam and you have to pass it.
Coming to engineering, then yes it will be there. they will give you admission you based on your skills and performance. They will have their own process to test candidates. If you qualify in it then you will get an admission. It can be your score in state level entrance or national level entrance. You have to appear one to get an admission.
Hope it helps!
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