Engineering Entrance Exam

The answer vary as the definition of good college depends on you, I know some who are repeating even after getting 4k rank in JEE Advanced. Let's make a list of good options ( in my opinion)
Creamy layer (CSE, ECE, electrical, mechanical)
NIT Trichy
NIT Warangal
NIT Surathkal
Better NITs ( CSE, ECE, electrical)
NIT Allahabad ( chemical is also famous branch of Allahabad because of its location near chemical industries of Uttar Pradesh)
NIT Rourkela
NIT Jaipur
NIT Calicut
NIT Nagpur
Other good NITs ( only CSE and ECE)
NIT Bhopal
NIT Surat
NIT Jamshedpur ( mechanical is a good option because of location)
NIT kurukshetra, Jalandhar, durgapur, Hamirpur, Delhi
NIT Patna
Other NITs
Okay, now let's discuss the cutoff :- ( all cut-offs are for other state)
Creamy layer (upto mechanical)
General = 9900 Marks= 175
OBC NCL =3300 Marks= 154
Better NITs ( upto electrical)
General= 12500 Marks=155+
OBC NCL= 3900 Marks 142
Other good NITs ( upto ECE)
General=20000 Marks= 141
OBC NCL=6000 Marks=134+
Here the marks mentioned are approximated using the last two JEE Main sessions ( Jan and September 2020). The marks required for EWS and OBC candidates are almost parallel for all india quota so one can get the idea for EWS.

You can apply for the EWS category if you have a lower percentile, provided you have related documents and have given MHT CET with the EWS category. Since there is a reservation for EWS candidates in Maharashtra (MH-CET), the cutoffs for colleges are generally lower than for general category students. For instance, in the previous year, in Amravati College of Engineering, students were allowed admission with a rank of 23,000 in the EWS category (MH-CET), whereas the general category students needed to be ranked under 9,000 for admission. Therefore, you can have comparatively better chances of getting admission. However, you must be eligible for an EWS seat, or else your admission will be rejected.

No, you do not need to give the Jain Entrance Test JET to get admission into the Jain University for a B.Sc. Degree course. The reason is because this exam is conducted by Jain University for admission to B.Tech courses only. The university offers a Bachelor of Science in around 32 specializations, and you have to meet the basic eligibility criteria, which is: (a) You must have passed the 12th grade at a recognised board. (b) You should have scored more than 40% in the relevant Science subject at 12th-grade level. If you fulfill this criteria, you may directly apply online on the university website. However, final admissions will be based on merit in the 12th grade, and if you scored higher than 75%, you have a good chance of getting into this college.

Your strategy totally depends upon your goal, and upon your situations. Speaking about a general, non-ews student, you need a percentile greater than 92, for which you'll only get a seat in the spot round, for biotech or mpae at NSUT/NSIT. Marks anywhere around 110 to 120 could be enough, considering the exam is now of 300 marks. Strategies that could work would be -
Download subjectwise JEE Mains archive for previous years. Revise the notes/formulas/questions practiced of a particular chapter of your choice each day and then attempt just the JEE Main part of archive only (leave out the JEE advance questions), and complete 1 to 2 chapter (for Physics and Maths or upto 3 to 4 (for Chemistry each day. Try to analyse what mistakes you made and how would you correct them, the very same day. Just simply watching the solution on YouTube or on Google will be enough. After a month, you would have covered most of the syllabus considering you do as said sincerely. Now download all the 16 question papers of JEE Main 2019 and the 8 question papers of JAN, 2020. Attempt 2 complete tests each day and don't forget to learn from your mistakes. Before starting your tests each day, just revise formulas or notes for any 5 chapters of your choice. And next 5 the following day and then similarly the next. By doing this you'll not forget formulas and also learn how to attempt the exam simultaneously. Leave everything on the day before your actual exam and just relax and have faith in your hardwork. I used this strategy myself last year and was able to get a 96+ percentile. All the best!