Lateral entry

Candidates who want admission in B.Tech lateral entry should possess a Diploma of three years in any branch of engineering from recognised university. The candidates should secure a minimum of 60% (50-55% for SC/ST) marks in all the semesters as an aggregate.

Hi, Lateral entries are for Diploma holders and not for B.Tech 1st year students,so you cannot write the exam. As far as college swapping is concerned you can switch colleges under the same university if you have some legit reasons but the chances are very slim.

Hello,
You can visit this link for the admission.
https://www.shiksha.com/b-tech/course/b-tech-in-polymer-engineering-lateral-entry-b-s-abdur-rahman-crescent-institute-of-science-and-technology-vandalur-chennai-298180

Kindly visit this link
https://www.shiksha.com/college-predictor

Most states will provide. So do some research and find out the best college for you.

The candidates who have completed DPT course conducted by the paramedical board are eligible for admission to BPT course in lateral entry.
BPT Eligibility Criteria
A Minimum aggregate score of 50% or equivalent at 10+2 level is mandatory for admission. Some universities in India conduct an entrance test for admitting students for the BPT course.

https://www.shiksha.com/college/tickoo-institute-of-emerging-technologies-gurgaon-34997/questions.

You can get admission in COEP ( B.Tech lateral entry ) only through Diploma, not through B.Sc.