Hmm, try something like this:

#!/usr/bin/perl -w

use strict;

my $input_file = "ipnum";
my @array;

{
    local *INPUT;
    open(*INPUT, $input_file) or die "Cannot open: $!";
    @array = <INPUT>;
    close(*INPUT) or die "Cannot close: $!";
}

foreach my $address (@array) {
    my $output = `nslookup $address`;
    print $output, "\n";
}
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This does a few things your code doesn't. First, it enables warnings (-w) and uses the strict pragma. These will help you detect errors and help you become a better Perl programmer. Next, it creates a local filehandle, named INPUT, within a block -- just a good idea if you this will ever be part of another program. It also dies, displaying error messages, if the open or close calls fail -- very important. Always check these calls. $! is your friend here. The rest of it should be pretty self-evident. (Especially after the ever-vigilant btrott pointed out a couple of errors and I corrected another.)