Colleges in Karnataka

Yes, you can find the VTU (Visvesvaraya Technological University) syllabus for B.Tech Data Science for all semesters on the official VTU website. Here are the steps to find the syllabus:
Go to the official VTU website: I can't post here (against community guidelines)
Click on the "Academics" tab on the top menu.
Under the "Academics" tab, click on the "Syllabus" option.
On the syllabus page, select "B.E/B.Tech" as the course.
Then select "Data Science and Engineering" as the branch of study.
Select the semester for which you want to see the syllabus.
The syllabus for the selected semester will be displayed on the screen.
You can repeat these steps for all the semesters to download or view the VTU syllabus for B.Tech Data Science.

The admission process for CS and EC courses in different colleges through KCET may vary based on several factors such as the number of available seats, the cutoff ranks of the college, and the number of students applying for these courses. So, it's not possible to predict with certainty whether your cousin will be able to get admission to a CS course or you will be able to get admission to an EC course based solely on your KCET rankings.
However, based on previous year's admission trends and cutoffs, it is possible to get an idea of the chances of admission. Generally, a KCET ranking of 55,000 may be sufficient to get admission to a CS course in some colleges, while a ranking of 67,000 may be sufficient to get admission to an EC course in some other colleges.
It's recommended that you and your cousin check the cutoff ranks for CS and EC courses in the colleges you are interested in and compare them with your respective KCET rankings. You can also consider participating in the counseling process to explore all available options and increase your chances of getting admission.

The current placement data of Amrita Chennai campus. However, I could suggest that the placements in a particular campus can vary based on various factors such as the industries in the location, the reputation of the college, and the quality of the students. Regarding the difference between Chennai campus and other campuses, each campus of Amrita has its own unique features and strengths. However, they all follow a common Vision, Mission, and Goals, and the curriculum and standards are the same across all campuses. It is always better to talk to the respective campus authorities or alumni to get a better understanding of the placements and other details.