Law Entrance Exam

Yes, you can take admission in 3 years LLB course without having to appear for entrance exam. There are colleges who offer admission on the merit basis.
LLB is a 3 years long course which has started to be replaced by BA LLB course which is 5 years long. Most colleges these days are preferring to offer BA LLB course to the candidates which can be taken after completing 12th standard. It is mandatory to appear for entrance exam for BA LLB course. The name of entrance exam is CLAT.
There is however no such requirement for LLB course. You can seek direct admission based on the merit. You will have to appear for an interview after which you will be given admission for LLB course.
Although not every college follow this procedure and a large number of them prefer to select candidates through entrance exam. The criteria for entrance exam is:
Eligibility
1. A Bachelor degree in any stream.
2. Minimum of 45 percent marks in Bachelor degree.
3. SC/ST need 40 percent marks.
4. Age limit for LLB is 30 years.
5. SC/ST gets 5 years relaxation in upper age limit.
The criteria for admission based on merit is also same. However you will need to have good percentage to make the cut. Below are some colleges that offer admission through merit.
1. Government Law College (Mumbai)
2. Balaji Law College (Pune)
3. ILS Law College (Pune)