hello lakshay khanna ,

national level entrance exam is JEE mains for btech .

there are many state level or college conductes their own entrance exams .

Hi

It depends from college to college. Nowadays most of the Engineering colleges application is online mode. 

For eg all the priviate university application is available only in online mode.

Some colleges have application form in offline mode. Here you will have to go the college and fill the form with pen and paper.

Most of the state run colleges are still sticking to offline mode.