With the rank that you scored it nearly impossible to get ant core branches seat at VIT Vellore or Chennai campus, So you can try for Chennai campus with lower category fee structure in order to get a decent branch but only if you go till 5th category fee structure then chances are there that you’ll get a seat at Chennai campus.
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No its not possible to get CSE seat at AP campus under category 1 based on your rank , you might need to go upto category 3 to be on the safer side to get confirm CSE seat.
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Yes you can get any of the campus as youre only eligible for these two campus only. In order to get core branches youll have to do choice filing till category 3 fee structure .
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With a VITEEE rank of 10,798, it is unlikely that you will secure a Computer Science Engineering (CSE) seat under Category 1 at any VIT campus, including VIT Vellore or VIT Chennai. Based on past trends, CSE seats in Category 1 close by around the 8,000-9,000 range at VIT Chennai. However, you may still have a chance in Category 2 or higher categories, where cutoffs extend up to around 14,000 for CSE. It would be best to explore these options during counseling.

For more details you can visit the link given below

https://engineering.careers360.com/articles/viteee-cutoff