IIIT

With a rank of 64,000 in JEE Mains under the general category, admission to the top IIITs will be difficult as their cutoffs are usually on the higher side. Yet, there is a possibility of getting admission to some new or lower-ranked IIITs or other state-level engineering colleges.

It may be difficult to get accepted into prestigious IIITs or government institutes for key fields like computer Science electrical engineering or mechanical engineering if you are an EWS girl candidate with a JEE Mains CRL rank of 290,000. But you can think about choices like:

Government-sponsored Technical Institutes (GFTIs): The threshold for some GFTIs might be lower.
State Government Colleges: For EWS applicants in particular several state engineering colleges provide favourable possibilities with state quotas.
IIITs: There may still be opportunities at less established or competitive IIITs that provide core branches.

The IIIT UGEE, or International Institute of Information Technology Hyderabad Undergraduate Entrance Examination, is the entrance examination held by IIIT Hyderabad to seek admissions to its dual degree courses like B.Tech and MS. It is an annual three-hour computer-based examination. It consists of two components- SUPR, dealing in subjects Physics, Chemistry, and Maths and REAP testing candidates for research aptitude skills and, through their performance in both of these, they are screened by a process of interview before joining.

No, you can't get admission to IIIT Lucknow for BTech unless you qualify for JEE Main. For the undergraduate courses, JEE Main is the mandatory entrance exam, and admissions are made through JoSAA counseling based on ranks in JEE Main. But for other courses like M.Tech, MBA, MSc, or PhD, different entrance exams need to be qualified for; for example, GATE, CUET PG, IIT JAM, respectively. Most of the courses in IIIT Lucknow do not allow direct admission without an entrance exam.