Engineering Entrance Exam

SRMJEEE is actually not a very tough exam when compared to JEE Mains, BITSAT, etc., but that doesn't mean things can be taken for granted either, particularly taking into consideration the heavy competition that there is for such exams. So, read further to gain an insight on the little you could do to crack this little nut of an exam with a really good rank.
First of all, take a look at the syllabus that is given to you in the SRM prospectus. Most of it would be the same as your class 11th and 12th PCM syllabus. If you are a CBSE student, you will find that they are exactly the same topics as in the NCERTs.
Next, try to gain a good conceptual understanding of the same and then work out certain numerical problems in each of the topics in Physics and Chemistry (if any) and selected problems in Maths. Just so as to revise the concepts (try to concentrate on the areas you had trouble gaining clarity during the boards and work to clear them).
Try solving the sample papers provided in the prospectus or the website, if time permits. If you are already undergoing some sort of coaching for the JEE Mains, I believe this should not be hard for you and you would perhaps be accustomed to tougher papers.
After you have done all this (if you have done half of all that I have mentioned above, this exam is still going to be a calk walk), just keep calm and take your exam. Mind you, there is negative marking in SRMJEEE, unlike the VIT entrance test.

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.

The crux of all the major engineering entrance exam that a student prepared or is essentially the same. They all focus on concepts of physics, chemistry and maths. The difference is only in the level of difficulty.
JEE is definitely the highest and the toughest when it comes to the level of difficulty and it tests you on applying multiple concepts in a single question. In addition to that, it also tests your endurance as an engineering aspirant. If one prepared for an exam like JEE, one can be rest assured that all the parameters of your preparation are being covered as JEE is the most exhaustive among the entrance tests.
So, one does not need to prepare separately for VITEEE as your fundamental preparation is already done. What one can do additionally is:
1. Go through past year papers of VITEEE to see the level of difficulty.
2. Take times mock sets for VITEEE. This is important because, in easier entrance exams, time management becomes a matter of paramount importance as the cut-off is higher. So, you need to answer more questions with higher accuracy.
Apart from this, no additional or separate preparation is needed.

No, you don't need to prepare for MUOET separately if you are preparing for JEE exam. MUOET paper is quite easy as compared to JEE paper. You just have to solve mock papers of MUOET to get an idea of paper pattern and quality as well as the quantity of questions asked.
Syllabus of both the exams is almost similar. Physics, chemistry and mathematics are common in both the exams. But MUOET asks few questions of English and aptitude.
Again, the level of aptitude and English is not too high, you can easily prepare for it in one or two months before the examination. You can take a lot of mock papers to boost your confidence.
NCERT is enough for chemistry and for physics part, you may prefer HC Verma. You may refer RD Sharma MCQ for maths.
MUOET is not that hard nut to crack, so even if you have prepared/finished 50% syllabus of JEE then you can easily crack it. So don't worry about MUOET and prepare for JEE with full confidence and determination.
Hope it helped.