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Hi. Admission Process for BVSc
Admission in the undergraduate Veterinary course is based on the entrance exam results. However, to be eligible for the entrance examination, one must have a minimum score of 50% in class 12th with Physics Chemistry and Biology as compulsory subjects. The dates of admission processes for the academic year 2022 will be out shortly. So keep a regular check on the official pages of the universities that match your preference. BVSC Admission 2022: Your Step by Step guide
Follow the following steps to apply for a Bachelor's degree in Veterinary Sciences. Check the eligibility criteria and appear in the BVSC entrance examination. After the shortlisting, admission to the colleges will start with the counselling round. Fill the college choices very carefully in the counselling round. As per the examination score and the admission quota, college admission will be offered. Accept the admission offer. Make the payments for admission and secure your position. The application dates and deadlines will be out soon on the official websites of the concerned colleges and universities. Eligibility criteria
The minimum Eligibility Criteria for admission in BVSc:
The candidate needs to have completed 12th standard with Physics Chemistry Biology the makers navigate and English as a compulsory subject. The minimum age for admission in BVSC is 18 years. However, the maximum age limit goes up to 25 years. Relaxation of one year is provided for reserved category candidates in terms of age. And the relaxation of 5% in terms of marks is provided for scheduled caste and scheduled Tribes and other reserved category candidates. BVSC Entrance Examinations
The All India Pre Veterinary test (AIPVT) was considered for admission to Bachelors for Veterinary Sciences. However, since 2017, NEET scores are considered for admission to BVSC.

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.

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.