TNEA

The answer is no. You cannot get into SRM through TNEA.
Anna University conducts Tamil Nadu Engineering Admissions (TNEA) to offer admissions to candidates in various engineering colleges in the state of Tamil Nadu. TNEA counselling is a single window process and admissions in Tamil Nadu engineering colleges are offered through such a process because authorities believe that such an initiative facilitates transparency.
Here is the list of colleges that accept TNEA scores: https://www.shiksha.com/b-tech/articles/tnea-2014-list-of-tamil-nadu-engineering-colleges-blogId-8105
Sri Ramaswamy Memorial (SRM) University conducts Sri Ramaswamy Memorial University Joint Engineering Entrance Examination (SRMJEEE - UG) to offer admissions to interested candidates in its B.Tech programmes.SRM University also conducts SRM Joint Engineering Entrance Exam (SRMJEEE) through which it offers admissions to candidates in programmes like Health Sciences. Candidates can appear for SRMJEEE either through the paper-pencil mode or even as a computer-based exam.
So for getting into SRM, you need to give SRMJEE.
Sources -
https://www.shiksha.com/b-tech/exams/tnea
https://www.shiksha.com/b-tech/exams/srmjeee-ug

VIT, Vellore accepts admission only through VITEEE.
For more details about its eligibility, you may refer to the link mentioned below:
https://www.shiksha.com/university/vit-university-vellore-29714/admission#admission
Vellore Institute of Technology (VIT) University conducts Vellore Institute of Technology Engineering Entrance Exam (VITEEE) to offer admissions to aspirants in B.Tech programmes available at its Vellore and Chennai campuses.
VITEEE is a computer based test (CBT) and its language of instruction is English only. The duration of this entrance exam is two and a half hours.
Apart from exam centres in India, VITEEE is also held at two international test centres which are Dubai and Kuwait.

Hello Gokul,
It is really good that you have got automobile engineering at PSG Tech, Coimbatore as it is one of the top colleges for doing automobile engineering.
It has its own industry and so you cannot get a better option.
PSG is known for its mechanical related courses like automobile engineering as the placements are really good and many good companies do come.
People may say that automobile engineering has no scope in future but automobile forms an essential part in our life. As long as cars, bikes, buses, etc. run on the roads, automobile engineering graduates will be having scope.
But it is necessary to adopt for the current trends like self-driven cars, which will not be in the curriculum. Just get updated and learn more.