Rhetorical Question: What's different between the two examples? My Answer: You lost your quote marks around the command being sent to cmd /k, so the && was being processed by the system-level cmd.exe rather than the embedded one.

Here, I will use the qq{} double-quote notation to nest the quotes, so interpolation will still happen properly:

my $cmd = "perl Perl_Ex_1.pl";
system(qq{start cmd /k "cd c:\PerlExamples && $cmd"});
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Thus, system runs the whole command (everything within the qq{}), and cmd /k runs everything in the normal quote characters (so both the cd and the $cmd).

update: edited first paragraph for clarity