Yes, you often need to take an admission exam in order to pursue B.Com. LLB. Depending on the university or law school, admission criteria may change, however the majority of them need passing one of the following entry exams:

Tests of Common Entrance for B.Com. LLB: Common Law Admission Test (CLAT):

for entry into other private universities as well as National Law Universities (NLUs).
includes topics such as mathematical aptitude, general knowledge, logical reasoning, and legal reasoning.
The All India Law Entrance Test, or AILET:

carried out by Delhi's National Law University.
It is unique to NLU Delhi, but it follows a framework similar to that of CLAT.
Law School Admission Test, or LSAT India:

approved by a large number of Indian private law schools.
emphasises analytical reasoning, logical reasoning, and reading comprehension.