Hello Shivani,
The application procedure for each university is different.
Considering that you filled the application form online and also paid the application fees through online banking, you most likely do not have to submit the hard-copy of your application form.
When the university calls you for document verification and counselling process, that is when you have to take the printed application form alongwith your other documents for verification.
So yes, you should download your application form and keep atleast 2 printed copies with you in case you need them.
If you have more doubts then you can contact the university and ask them the next step, they will guide you.
Hope this helps.
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile