Exam

Yes VIT, Vellore accept NMAT score for its MBA courses. The detailed eligibility criteria is given below. Eligibility criteria: A minimum of 60% mark of First class is required in undergraduate degree from a recognised University or Institution. A Bachelors degree should be of minimum of three years duration after completion of higher secondary education (10+2) or equivalent. The candidate should have studied in regular full-time programmes. The candidate should have taken any one of the tests- CAT/XAT/MAT/NMAT/GMAT/CMAT/ATMA and the scores should be made available to the admissions office before the last date of application. Selection process : Selection of candidates is based on the Written Assessment Test (What), Personal Interview (PI) and CAT / XAT / MAT/ NMAT/ GMAT/CMAT/ATMA Score. The flowing are the other colleges accepting the NMAT scores.
1. Thapar School of Management, Mohali
2. University of Petroleum and Energy Studies (UPES), Dehradun
3. Amity Business School, Noida
4. SRM School of Management, Chennai
5. IBS Hyderabad.

Yes you can apply for VIT exam for following courses. Candidates who have (Biology / Physics / Chemistry) in +2/ Higher Secondary Board are eligible for the following Bio stream programmes only. But after joining, registering Mathematics as bridge course is mandatory.
1. B.Tech. Bio-engineering (VIT-Bhopal)
2. B.Tech. Computer Science and Engineering with specialisation in Health Informatics (VIT-Bhopal)
3. B.Tech. Biotechnology (VIT, Vellore)
4. B.Tech. Computer Science and Engineering with specialisation in Bioinformatics (VIT, Vellore)
5. B.Tech. Electronics and Communication with specialisation in Biomedical Engineering (VIT, Vellore). .

Due to the Covid-19 pandemic, VITMEE has been postponed for this year. Direct admission is given to GATE qualified candidates, while Non GATE candidates will be admitted based on academic records (up to pre final year performance). The syllabus of VITMEE for EEE is given below.
1. Engineering Mathematics (Linear algebra, Calculus, Differential equations etc.)
2. Electrical engineering (Electric circuit, Signal and system, Electromagnetic field etc.)
So syllabus does not covers the analytical and logical sections. however the English communication syllabus is common to all PG courses.
For books you may refer to the syllabus and read the B.Tech books.

All India MCA Common Entrance Test (AIMCET) is conducted by IIT. It is one of the most important and well-known entrance examinations across the country. Candidates can apply for AIMCET 2020 to provide the admission to deserving candidates in MCA Master of Computer Science at IIT. By appearing and qualifying this entrance examination, one can get the best colleges across the country for the education of MCA. Application availability : January-February 2021
Examination Date: June 2021
Eligibility Criteria : A graduation degree from a recognised university with a combination of Computer, Maths, Physics, and chemistry is required. The subject Mathematics is compulsory in class 12th or Graduation level. While NIMCET is for admission in MCA course in NITs. The NIMCET is a Common Entrance National Level Test, conducted by any of the NITs, for admission in to their MCA programme. The MCA programme is offered by NITs at Agartala, Allahabad, Bhopal, Calicut, Jamshedpur, Kurukshetra, Raipur, Surathkal, Tiruchirappalli and Warangal. The admission into the MCA programme for the year 2020-21 in above 10 NITs is based on the Rank obtained in NIMCET-2020 only. The probable dates of NIMCET 2021 are given below. Opening date for online Registration: First week of March 2021
Entrance exam date : Last week of May 2021
Eligibility Criteria to Appear For NIMCET-2021 : Indian Nationals securing at least 60% marks in aggregate or 6.5 CGPA on a 10-point scale (55% marks or 6.0 CGPA on a 10-point scale in case of SC/ ST/PwD) in (I) B.Sc. / B.Sc. (Hons) / BCA / BIT / B.Voc. (Computer Science/ Computer Applications) of minimum
three years full-time programme from a recognised University with Mathematics/ Statistics as one of
the subjects
or (ii) B.E. / B.Tech. From a recognised University
So you can plan accordingly.