if ($string =~ /[^A-Z0-9]/) {
   # String contains a character other than A-Z, 0-9.
   ...
} else {
   # String only contains characters A-Z, 0-9.
   ...
}

##</code><code>##

if ($string =~ /^[A-Z0-9]*\z/) {
   # String only contains characters A-Z, 0-9.
   ...
} else {
   # String contains a character other than A-Z, 0-9.
   ...
}