JEE

Yes, with a 54k rank in JEE Mains with a valid EWS certificate, you can definitely get any college through JoSAA counselling. Although it is difficult to predict the college, but the probabilities of getting a decent college with your score are very high. You can register by visiting the official website of JoSAA and fill your choice and preferences along with your score card. You'll be allotted your seat based on your score and preferences followed by counselling rounds and documents verification. 

Thus JEE Mains cutoff for BSc in IIT Patna differs from category wise and course wise. Hence for general category the qualifying Rank for BSc in Mathematics and Computing is 3252 – 4952. But, IIT Patna does not provide the normal BSc programme for those students who want to study BSc degree. Instead, it includes composite courses such as B.Tech + M.Tech or BSc + MBA etc. The competitive course cutoff ranks vary between 1760-2985 for the Computer Science and Engineering, 2764-4346 for Artificial Science and Data Science, and between 515-556 for BSc programs.

Yes, you can join Hindusthan College of Engineering and Technology BTech without any JEE Main score. As per the admission guidelines sanctioned by HICET admission to the BTech course is subject to the last qualifying exam and entrance exam score. The College accepts multiple entrance exams other than the EE Main exam. Candidates with exam scores in HTSEE or TS EAMCET are eligible for the BTech course at HICET. 

With a JEE percentile of 40, the options for admission to engineering colleges are very limited. You would probably not get admission in NITs or IIITs, but you could think about private engineering colleges or state-level institutions. You would probably look at lower-tier private colleges that take higher ranks or management quota seats. The other options are colleges that take students based on intermediate merit. Institutions in States like Madhya Pradesh and Uttar Pradesh may also have openings. Always check the specific admission criteria and processes for each college during counseling.

You can see that, with a JEE percentile of 51 and a rank of 729,689, B.Tech in Computer Science Engineering may not be a choice for you. The private college or university which is the lower-tier option might allow higher ranks. The following may be the choices available to you: Shivaji University, especially for its engineering courses, Bharati Vidyapeeth Deemed University, where you may get the course that you are interested in studying, and PES University. It is prudent to engage in counseling process and explore available seats in various engineering disciplines since various colleges have different cutoffs.

With a 72 percentile in JEE Mains, you may have a fair chance of getting a seat in a few NITs, and this is not a guaranteed possibility as a rank around 286,000 to 322,000 corresponds to this percentile, and so the prospect of getting admission in premier NITs is impossible. However, there could be a possibility in lower ranks of NITs where cutoff is relatively relaxed in the case of ST students. It is advisable to go for counseling and explore state-level colleges as well, which would be more lenient regarding your percentile range.

With your JEE Mains score of 83.6% and IPE marks of 911, you can apply to SASTRA University under Stream 1, which considers both JEE Mains scores (25% weightage) and board marks (75% weightage). The exact eligibility depends on the specific course and competition in that year. For Stream 2, admission is based solely on board marks, with higher marks (90%+) improving chances for competitive courses.