Hi

Unless the mode of the entrance exam is ORPE( online remote proctored exam) you can't take it from home irrespective of you being ill or not. This year Vellore institute of technology had conducted it in ORPE. Same can't be said about in 2022, they might be taking it in centers all over India. Check this link

https://engineering.careers360.com/articles/viteee-exam-centres

As for AEEE it is both computer based and ORPE based , meaning you can take it in centers allotted or from home, both will be computer based.

For more check this link

https://engineering.careers360.com/articles/aeee

Hope this answers your query!