Engineering Entrance Exam

With a rank of 264982 in the general category, options for admission to engineering colleges may not be very high, but they are still there. Here are some colleges that you may consider:
Private Engineering Colleges: Many private institutions have lesser cutoff ranks and may accommodate students with higher ranks. For example:
Shivaji University, Kolhapur
MIT College of Engineering, Pune
Bharati Vidyapeeth Deemed University, Pune
Some of the State Engineering Colleges do have openings for students of higher rank particularly for less popular streams.
Government Funded Technical Institutions: While a highly competitive list, some of the GFTIs may have a few seats opening up for the students who have a rank higher for that particular engineering stream. Counselling is a must and each college cutoff may vary in its requirement of rank in the entrance exams.

To be qualified for JEE Advanced, one must fulfill certain specified criteria like clearing the JEE Main exam with ranking among the top 2,50,000 candidates. If you got 86.35 percent in the JEE Mains B.Arch exam, you need to check if your rank comes in that bracket. In addition to that, candidates must also clear their Class 12 examination with Physics, Chemistry, and Mathematics as compulsory subjects.
Since you are interested in B.Arch, then you must also satisfy any additional eligibility criteria related to the drawing test. If your rank fits within the top 2.5 Lacs and you otherwise qualify, then you should be eligible to appear in JEE Advanced.

You have an 87 percentile score in JEE Mains as a female in the General EWS category; here are some engineering options for you, that are either from or near Maharashtra:

Vishwakarma Institute of Technology (VIT), Pune: Very strong in engineering: Usually requires a percentile around yours to qualify.

MIT World Peace University, Pune: This university brings you a lot of engineering programs; it guarantees admission for students at this percentile.

Sardar Patel Institute of Technology (SPIT), Mumbai: Highly competitive but sometimes accepts students at your level, especially in the EWS category.

Thakur College of Engineering and Technology, Mumbai: This institute usually has cut-offs in the range of your score.

KJ Somaiya College of Engineering, Mumbai: Another college in which you might possibly get admitted based on your percentile.

You might be able to get admission into DTU with a 71 percentile in JEE Mains, 60% in your 12th grade, and from the SC category. Some key points related to eligibility:
Eligibility: To seek admission to B.Tech in DTU, one has to have passed Class 12 with aggregate percentage not less than 60%. The combination is PCM, however for SC students, there is relaxation and often the minimum percentage is considered.
JEE Mains Score: Admissions are mainly offered based on the scores of JEE Mains, which will be considered by the JAC Delhi counseling process. Your 71 percentile would be competitive for some streams, so ensure to see the precise cutoffs for this year.
Counselling Process: It will book only a seat after you participate in the counseling process of JAC Delhi. The final admission will be according to the rank you have, and there are also seats available in the branch you want to pursue.

Yes, if you get good ranking (below 3000) in SRMJEEE exams, then you get the scholarship that reduces your fees; in fact, there are some scholarships based on JEE rank categories at SRM University: for example,
Rank-Based Scholarships:
Students ranked 1001 to 3000 can be accorded a 25% scholarship on tuition fees.
Up to 75% or more may qualify for higher ranks, such as 101 to 500.
The rest of the awards go to very meritorious students and other criteria set for scholarship. It would be essential to apply for the scholarship while undergoing the admission process as well as fulfilling any set stipulated conditions. For exact details, refer to their scholarship policy at SRM or to the admissions office.

Getting admission in NITs for B.Arch and B.Planning depends upon percentile as well as the factors like your category, seat availability in the respective state and state quota for SC/ ST/ OBC students which surpass 90.6 percentile in B.Arch and 92.4 percentile in B. Planning in JEE Mains Paper II.

For B.Arch and B.Planning, it depends on the Gen cateogy students throwning out their percentage so as to explain the NIT cutoffs. Commonly it varies from 94-98 percentile for top most NITs like NIT Trichy and NIT Calicut only. However, for NC-OBC, SC, and ST categories, the cutoff can be low about 85- 92 percentile.

You might get through in the lower ranking NIT's or under Domicile Quota if available in the NIT's. Going to the rounds of CSAB may seem to work better regarding getting seats for studies.