#!/usr/bin/perl
use 5.014;

my @ar=('abc10', 'abc11', 'abc01', 'abc02', 'abc111'); 
for $_( @ar ) 
    {
    if( $_ =~ /^abc[10]{2}/Z/ ) # wrong; see below 
        {
        say $_;
        }
    }

##</code><code>##

983013.pl
abc10
abc11
abc01