my $dna=();
 foreach my $dna (@random_DNA) { # Line 19 
   print"$dna\n";}  
 print"\n";# one per line Line 21
my $output="RandDNA .txt";
unless (open(RESULT,">my $output")){
print"Cannot open file\"my $output\".\n\n";
exit;
}  # Line 26  
print RESULT"\n Randomly Generated dna:\n
 The DNA set containing $number molecules varying in length from $minl
+ to $maxl bases are:\n\n
 my $dna\n";
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The first line creates the variable $dna with nothing in it (the undef value) and the print at the end trys to print this value resulting in a warning message.    The second line creates a variable named $dna that is local to the foreach loop so the print inside the loop will only produce a warning message if @random_DNA contains an undef value.

my $number= <STDIN>;

my $maxl= <STDIN>;

  my $minl= <STDIN>; # Line 10
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You should chomp values you receive via the readline operator.

  srand(time|$$);
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Unless you have a really really REALLY old version of perl you shouldn't use the srand function.

 my $dna;                        # Line 40
 # Set of DNA fragments 
 my @set;                        
 # Create set of random DNA:  
  for (my $i=0;$i<$number;++$i) {
 # find a random length between min & max Line 45:  
  $length= randomlength ($minl,$maxl);
 # add $dna fragment to @set Line 47:  
  push (@set,$dna);}
  return @set;}  # Line 49
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On the first line you create the variable $dna with nothing in it (the undef value) and then push that value into @set many times and then return a list of those undef values.

# Now write the subroutine make_random_DNA:
sub make_random_DNA {                      # Line 57      
 # Collect arguments, declare variables:
 my ($length)=@_;                          # Line 59  
 my $dna;
 for (my $i=0;$i<$length;++$i) {
 $dna.=randomnucleotide();}                # Line 62   
 return $dna;}
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This subroutine never gets used anywhere so no random DNA sequences are created.

This may work better, at least it's easier to read (UNTESTED):

#!/usr/bin/perl
# Program to generate Random DNA set:
use strict;
use warnings;


print "\n\n Enter No. of DNA Molecules required: ";
chomp( my $number = <STDIN> );

print "\n Enter Maximum length of DNA (bases): ";
chomp( my $maxl = <STDIN> );

print "\n Enter Minimum length of DNA (bases): ";
chomp( my $minl = <STDIN> );


# An array initialized to the empty list, to store the DNA in:
# Call the subroutine to do the real job:
my @random_DNA = make_random_DNA_set( $minl, $maxl, $number );

# print the results, one per line
print "\n The DNA set containing $number DNA molecules, varying in len
+gth from $minl to $maxl bases, are:\n\n";

print map( "$_\n", @random_DNA ), "\n";

my $output = 'my RandDNA .txt';
open my $RESULT, '>', $output or die qq[Cannot open file "$output" bec
+ause: $!];
print $RESULT <<RESULT;

 Randomly Generated dna:

The DNA set containing $number molecules varying in length from $minl 
+to $maxl bases are:

@random_DNA
RESULT

exit 0;


# Subroutines
# Calling the subroutine make_random_DNA_set
sub make_random_DNA_set {
        # Collect arguments, declare variables
        my ( $minl, $maxl, $number ) = @_;
        my @set;
        # Create set of random DNA:
        for ( 1 .. $number ) {
                # find a random length between min & max
                my $length = $minl + int rand $maxl - $minl + 1;
                # add $dna fragment to @set
                push @set, make_random_DNA( $length );
                }
        return @set;
        }

# Now write the subroutine make_random_DNA:
sub make_random_DNA {
        my ( $length ) = @_;
        my @nucleotides = qw( A T G C );
        return join '', map $nucleotides[ rand @nucleotides ], 1 .. $l
+ength;
        }
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