CSJM - Chhatrapati Shahu Ji Maharaj University

Yes, Chhatrapati Shahu Ji Maharaj University, Kanpur also known as Kanpur University offers B.A.+LLB (Hons) 5 years integrated course. The eligibility criteria is given below.
Eligibility criteria : 10+2 with minimum 45% of marks (40% for SC/ST)
Age : Maximum 20 years for general candidate and 22 years for SC/ST.
Admission criteria: Joint Entrance Test conducted by CSJMU
So, from above you need a minimum of 45% of marks in Intermediate or 10+2. Further, your dropout period will not affect if you are meeting the age criteria.

First of all, it is Shivaji Maharaj not Shakuni, and you can't take direct admission in this university, because it also conduct exam of their own.

Eligibility for BBA admission at CSJMU : Intermediate or 10+2 pass from U.P. Board or other equivalent examination of Arts, Science, Commerce, etc. Students appearing in intermediate may also apply subject to production of evidence of passing the examination at the time of admission. There is a written entrance test for admission conducted by CSJM University, Kanpur which will comprise of objective type questions on general knowledge, general English, arithmetic and reasoning. Group discussion and personality interview will also be held. Therefore, from the above, direct admission in BBA course is not available at CSJMU.

Students for various courses are selected through: Special Entrance Tests Interviews Their academic record Combination of the above.

https://www.shiksha.com/university/csjm-chhatrapati-shahu-ji-maharaj-university-Kanpur-23593
Refer the link.

For getting admission in law, you have to give CLAT exam and then only you can get admission.

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You have secured a very good rank and you should be able to get admission here in the first to second round of counseling.