Hello Ajay, you can do an integrated law course from Telangana state, considering that you want to do both law and degree together. You can do so, by appearing in an entrance test conducted by Osmania University on behalf of Telangana State Council for Higher Education, namely Telangana State Law Common Entrance Test (TS LAWCET).
Also your eligibility to appear in this exam, even after going for open inter exam in 12th depends on the eligibility criteria mentioned below.

Eligibility criteria for TS LAWCET 2019
For Five Year LLB Programme 

1. Candidate should have passed their intermediate examination ( 10+2 pattern) with at least an aggregate of 45%, or they must have cleared any examination equivalent to the Board of Intermediate Education, T.S, and Bar Council of India.
2. It has no age limit for the candidates
3. SC/ST category candidates will have to score an aggregate of atleast 40% in their intermediate examination.
4. Only the Indian nationals can apply for the entrance test.
Important note
Those candidates cannot apply for this entrance test who have done their 10+2 or graduation from open universities directly, without having any basic qualification for prosecuting such studies.
If you have done your 10+2 from an Open University, and the examination is not considered equivalent to the Board of Intermediate Education, T.S, and the Bar Council of India. In that case, you are not eligible for the course.
For any further information regarding your eligibility you can see through the link:
https://law.careers360.com/articles/ts-lawcet-eligibility-criteria
But if now you are planning to go for some other coveted entrance exam in the country, there are many like CLAT, AILET and IPU CET.
Then let me tell you that you must have cleared your examinations from a recognised board, either state or central or any equivalent exam. And you can go for these exams, but first read all their eligibility criteria, like marks required, age limit, chances for reappearing etc.
For queries about the above mentioned entrance exams feel free to ask.
All the best!
I hope this helps!