Yes, it’s possible to get admission to a law college in Mumbai without taking any entrance examination. There are several law colleges in Mumbai that offer admission to 3-year LLB degrees based on merit only. Here are a few such colleges.
Most law schools in India offer 5-year BA LLB degrees. To pursue it, you need to appear in CLAT after your 12th. Whereas for an LLB, you need to complete your graduation. Though in terms of job opportunities, there is no such difference between the two degrees.