After 12th you can go for 5 Years integrated programme only, you can not apply for LLB programme. The entrance exam you can appear on National level exams like CLAT, AILET & other university level entrance exam. To apply for the exam you should be 12th passed in any of the stream. You can check the eligibility to apply for the exams CLAT, AILET with given below link.

CLAT Eligibility

AILET Eligibility

Good Luck!