I think you may want to first decode the HTML and then encode the string as UTF-8.

use strict;
use warnings;
use HTML::Entities;
use Encode 'encode';

my $titlenamefromindex=q{ஸ்ரீசா&#x
+BA8;்த், சவான், &#xB9
+A;ண்டிலா ஆகி&#x
+BAF;ோர் தங்களத&
+#xBC1; குற்றங்க&#xBB3
+;ை ஒப்புக் க&#x
+BCA;ண்டதாக தகவ&
+#xBB2;&#xBCD};

$titlenamefromindex = decode_entities($titlenamefromindex);
print encode('UTF-8', $titlenamefromindex ), "\n";
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Output:
ஸ்ரீசாந்த், சவான், சண்டிலா ஆகியோர் தங்களது குற்றங்களை ஒப்புக் கொண்டதாக தகவல்

thank u

use HTML::Entities;
use Encode;

my $title_checking=$cgi->param("title_checking");

$title_checking=decode_entities($title_checking);
$title_checking=encode('UTF-8',$title_checking);

$title_checking=$prl->trim($title_checking);

print "$title_checking";
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It's working...In my server I stored this format value then compare it's working..great thanks

Are you definitely sure they are equal? One stray space or punctuation mark is all it would take for them to be different.

You should use modules such as Data::Dumper to find out, and perhaps reverse encode title_checking to see if you end up with the same entities.

In header section I used properly Meta content

    <meta http-equiv=\"content-type\" content=\"text/ html; charset=UT
+F-8\">
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In form section also i used properly utf-8

    <form accept-charset=\"utf-8\"></form>
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Next page param receiving

    my $title_checking=$cgi->param("title_checking");
    print "$title_checking";
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ஸ்ரீசாந்த், சவான், சண்டிலா ஆகியோர் தங்களது குற்றங்களை ஒப்புக் கொண்டதாக தகவல் Like that i receiving

I suggest just to be sure you walk along each character to find the difference. Something like this:

# there are probably better ways of doing a string diff...
my ($s1, $s2) = ($title_checking, $titlenamefromindex);

for (my $i = 0; i < length( $s1); $i++) {
   print "Different at $i\n" if (substr( $s1, $i, 1) ne substr( $s2, $
+i, 1);
}
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(You may need to make minor fixes to above)
If you spot any bugs in my solutions, it's because I've deliberately left them in as an exercise for the reader! :-)

$titlenamefromindex=encode_entities($titlenamefromindex,"\200-\377");

The variable $titlenamefromindex is already entity-encoded, and now you're double-encoding it. Are you sure that's what you want?