SMEAT

You may get seat in NIT Agartala , it depends on your category and branch preference. If you are an open category student them you cannot get any seat in any of the NITs whether it is gender neutral quota or female only quota.
It's possible that you get seat in EWS category or PWD category or OBC category or SC category or ST category that too it differs in gender neutral quota or female only quota.
Since you are category wise rank is 5105 you are eligible for some of the and IIITs and GFTIs in category reservation and gender neutral quota.
You won't get seat in NIT Agartala but you will get seat in IIIT Agartala in Computer science and engineering department.
You can check the college predictors using your rank and percentile so that you'll get a proper idea of colleges which you are eligible to get a seat and decide accordingly!!
Sure thing is that you cannot get a seat in NiT Agartala in any of the branch .
Better to go for IIIT Agartala , CSE if you are interested to join only in Agartala.
But in some cases you may get seat as you desired if you are Home State student for NIT Agartala( note: not always).

You may not get seat in NIT if your rank is 2.86 lakhs. But sometimes it depends on your category. There are few chances for getting into IIITs or GFTIs depending on your category. Getting seat in chemical or civil is difficult. You may get seat in least branches.But if you are Home State student of particular NITs or IIITs or GFTIs you may get a seat .
You will surely not get any seat in Josaa rounds . So you need to opt for CSAB special rounds so that you may get seat in some NITs or IIITs or GFTIs for some branches . Chemical or Civil is not a sure thing but sometimes you will get due to luck. It depends on the number of persons who have more rank than you appearing in CSAB rounds and number of seats left in those colleges in those particular branches .You'll have 3 options now:
Settle for some other engineering college and go ahead with its curriculum.
Settle for some other college and work for both your sem and next JEE prepration.
Join in some long term institutes and prepare well this time and give next JEE.

You have to fulfill the eligibility criteria for the respective programme to take admission at LPU. I recommend you kindly visit the LPU website for more details of programmes and their eligibility as per your interest. LPU has AA+ Infrastructure including shopping malls, refreshment centers, the largest Private University Accommodation in the world, 13000 + CC cameras, indoor transportation system, University Management System, etc. With Quality of Education, Placements in LPU is also amazing, with the top brand in the world coming for Campus Recruitment provides great opportunities to its students and because of its #ThinkBig concept and various innovations in curriculum, the university is standing tall and proud with various other very old and renowned institutions in terms of rankings and accreditation.

I guess you are asking for the fees of CSE, as in LPU there is no management quota. The Eligibility Criteria (Qualifying Exam) is Pass with 55% aggregate marks in Bachelors degree (any discipline) or equivalent, subject to qualifying LPU NEST or CAT or MAT or XAT or NMAT or CMAT^ and Interview
Mittal School of Business is among the first 10 institutions in India to get ACBSP (USA) accreditation, Mittal School of Business ranked among the top 40 Management institutions in India, as per NIRF ranking 2021. LPU is the only university that has tie-ups with leading companies. For example MBA (Business Analytics) in tie-up with WileyNXT, MBA (Financial Markets) in tie-up with NSE, MBA (Supply Chain & Logistics) in tie-up with safeducate. These are the unique features that make LPU the best private university for MBA. The curriculum is made keeping in mind the current market trends. The placements are 100%, and students have special placement-oriented classes that serve as a booster for students to clear the exam and interview. Companies like Hyatt, Ritz Carlton, Adani Wilmar, Altruist, Al-Rakha, and Dharam Consultancy selected LPU students for International locations. The highest package availed is 21 LPA.