Does Amdahl's law apply to modern multi-code processors? I was reading about Amdahl's law and it state that value of Amdahl's law always lies between 0 and 1. My question is, is it still true in today's case/scenario? When we have system like core i7?
Yes, it's still true. The speedup can't be less than zero (if parallelizing your code makes it slower, just run the serial version) or more than 100% (because saving more than 100% of the runtime would make the runtime negative).

Multicore processors are essentially just a matter of terminology changing over time. If you think you have one processor with four cores, Amdahl thinks you have four processors.