As others have said, if you want the results in a certain order, you need to specify that with an ORDER BY clause. I'd also like to point out that the way you go about gathering the array is more complex than it needs to be. If you SELECT both columns and use the DBI selectall_arrayref() method, you can capture everything at once like this:

my $results = $dbh->selectall_arrayref("
    SELECT MR_M,MR_R FROM MR2 ORDER BY MR_M LIMIT 10
");
for my $row(@$results){
    printf "%s\t%s\n",@$row;
}
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