First of all sugar++ for giving us sample input and reference output as well as a clear description of what your problem is.

In addition to what the others have said: You build a fairly large regex from @dels, which might slow down things (if the number of items is in the millions).

I'd suggest to use a hash instead of @dels:

#!/usr/bin/perl
use strict;
use warnings;
my $prev1=0;my $prev2=0;my @dels;
open my $file, '<', 'data.txt' or die "Can't open file: $!@";

my %dels;
while (<$file>) {
    # the \. prevents . from matching any character
    my @spl = split(/\.[fr]/, $_);
    if($prev1 eq $spl[0] && $prev2 eq $spl[1]){
        $dels{$spl[0]} = 1;
    }
    $prev1=$spl[0];$prev2=$spl[1];
}

# reset the file cursor, read from the beginning again
seek $file, 0, 0;
while (<$file>) {
    my @spl = split(/\.[fr]/, $_);
    print unless $dels{$spl[0]};
}
close $file;
[download]

This version gets rid of @arr entirely, and replaced the regex and @dels with %dels.

Going a step further, we can do this in a single pass:

#!/usr/bin/perl
use strict;
use warnings;

open my $file, '<', 'data.txt' or die "Can't open file: $!@";

my @prev = ();
while (my $line = <$file>) {
    my @spl = split(/(\.[fr])/, $line);
    if (@prev) {
        if ($prev[0] ne $spl[0] || $prev[2] ne $spl[2]){
            print @prev;
        } else {
            @prev = ();
            next;
        }
    } 
    @prev = @spl;
}
print @prev;

close $file;
[download]

thank u :) Now the program takes only 2 seconds to output the desired results :)

That's because you slurp the entire file into memory. It's better to step through the file line-by-line. It is more scalable and gives a better performance.

#!/usr/bin/perl --
# filter.pl

use strict;
use warnings;

die "Usage: perl filter.pl pe_real_sample.txt > last.output\n"
  unless @ARGV;

my %seen;
my @ary;

# push into @ary every line which have not be seen yet

while (my $line = <>) {
    $line =~ /[fr] / or die "Can't parse line: $line";
    my $key = $` . $';
    push(@ary, [$line, $key]) unless $seen{$key}++;
}

# print all lines from @ary having $seen only once

print $_->[0] foreach grep {$seen{$_->[1]} < 2} @ary;
[download]

This script can be written more shortly:

#!/usr/bin/perl -n
/[fr] /, $s{$`.$'}++ || push @a, [$_,$`.$'] }{ $s{$_->[1]}<2 && print 
+$_->[0] for @a
[download]

or even:

#!/usr/bin/perl -n
/f|r/,$s{$`.$'}++,push@a,[$_,$`.$']}{$s{$$_[1]}<2&&print$$_[0]for@a
[download]