B.Tech

Jain University issues the application forms online. Candidates must go through the website and determine eligibility before filling up the Jain University Application Form 2017. JET Application form 2017 are available at the respective constituent units from 16th November 2016, Wednesday between 10.00 hours and 17.00 hours. Forms are also available on http://www.jainuniversity.ac.in. It is essential that you have a valid email address if you are applying for the programme. To Apply Online for JET 2017
Applicants are responsible for submitting completed applications. If an incomplete application is received, it will be scrutinized on the basis of the information provided.

LEET is the entrance exam for candidates who wish to get lateral entry in the engineering colleges. Now I can't say if you can give LEET exam or not, because you have not mentioned any information about your course. Lateral Entry Scheme is basically for the candidates who have completed either Diploma in engineering or B.Sc.
Candidates can get direct admission for engineering course for second year. What kind of stream you can apply in engineering depends of the subject in which you have completed your B.Sc or Diploma. This scheme was started to give Diploma and B.Sc. Students a better career option. Since they won't be eligible to appear in entrance exams like IIT-JEE or AIEEE lateral entry scheme is the best option for them. There are two ways for lateral entry. Several colleges would give you direct admission based on your performance in Diploma or B.Sc. Course. Every engineering university in India reserves some seats for the lateral entry. They will either offer direct admission or via LEET entrance exam.
Source: http://entrance-exam.net/forum/general-discussion/can-i-give-b-tech-leet-exam-get-admission-2nd-year-896013.html#ixzz5F6tKeby0.