choroba did a great job fielding some of your coding issues. With some repeats, here's the following:

use strict;
use warnings;    #<<-- warnings

print "\n Enter The file name :>";
chomp( my $filename1 = <STDIN> );
open( FILE, "<", $filename1 )
  or die "\n...Cannot find the file: $filename1";    #<<-- $filename1"
open( W, "> Result.txt" );
my @line;
while (<FILE>) {
    push( @line, $_ );
    my $count++;
}
print W $line[0];
for ( my $i = 0 ;$i < $count ;$i++ ) #<<-- my $i; $count, from above, 
+has dropped outside of scope and is now undefined. Update: use $i < $
+#line+1
{
    my @st = split( ' ', $line[$i] );    #<<-- my @st
    if ( ( $st[4] eq /chr1/ ) && ( $st[10] eq /chr1/ ) ) {
        print W $line[$i];
    }
}
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Consider the following reworking (untested):

use Modern::Perl;

print "\n Enter the file name :>";
chomp( my $filename1 = <STDIN> );

open my $fh, '<', $filename1 or die "Cannot find the file $filename1: 
+$!";
my @line = <$fh>;
close $fh;

open my $w, '>', 'Result.txt' or die "Cannot open the file Result.txt:
+ $!";
print $w $line[0];

for (@line) {
    my ( $fourth, $tenth ) = ( split ' ' )[ 4, 10 ];
    print $w $_ if $fourth eq 'chr1' and $tenth eq 'chr1';
    # did you mean $fourth =~ /chr1/ and $tenth =~ /chr1/
}

close $w;
[download]

Hope this helps!