Hi,

Yes, you can go for Engineering after BCA. However, you will have to appear for admission only in private colleges where admissions are not on the basis of JEE Mains. The eligibility criteria states that a candidate is eligible for JEE Mains for only three consecutive years including the year in which you cleared 12th. For example, if a candidate has completed their 12th in 2019, then they can appear for JEE Mains 3 times, i.e, 2019, 2020 and 2021. Since, BCA is a three year course, you would not be able to apply for JEE Mains after that.

Here is a link that you can refer for more details for JEE Mains eligibility: https://engineering.careers360.com/articles/jee-main-eligibility-criteria

I hope this helped you.