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For admission you need fulfill the following criterion:-
The candidate should have been born on or after October 1, 1993 if belonging to the Open or OBC-NCL category and, on or after October 1, 1988 if belonging to the SC, ST or PwD category.
The candidate should have qualified, i.e., obtained a rank in UCEED 2018. The candidate should have passed the qualifying examination (Class XII or equivalent) in 2017 or 2018. Those who appeared for the first time in their qualifying examination in 2016 or earlier are not eligible.
For further details please refer this link: https://www.shiksha.com/design/industrial-product-design/exams/uceed/cutoff.

No, it isn't possible unless you are an NRI student because I have a lot of friends who didn't get admission because they did not give VITEEE exam.
There is no donation fee here. Let me explain you the system. The system is very simple, for a particular branch, there are few seats (eg. 250 seats) in first category. The first category could be understood as the seats given to the merit holders of VITEEE. The fees here is minimum and actually very cheap. Generally, VITEEE rank holders up to 20K can only contest for these seats. Then there is category 2 which again comprises of 230 seats and in this category, the fee is little high (you may say it includes donations in the fee). So, your fee for category two will be more for every branch and generally students over 20K rank contest test for these seats. When category 2 gets full rankwise, category 3 will be open and one can go and take a seat if her/his rank permits. One can get admission in VIT upto rank 90000 in any category. Hope this helps.