[exim] TLS issue with Exim 4.84?

Dear All,

I am running Exim4 4.84.2-1 on Debian Jessie. I was getting error while
sending mails to certain domains, but mails were going to domains like
gmail, yahoo etc. Then I installed a self certified certificate and a SSL
certificate and enabled TLS, assuming issue was with TLS. Still the
following errors are appearing when sending mails to certain domains.

++++++++++++ Log Start ++++++++++++++++++++++++++
2016-07-22 08:01:25 1bQQEs-0003xA-1d TLS error on connection to xx.xxx.com
[148.251.254.194] (recv): The TLS connection was non-properly terminated.
2016-07-22 08:01:25 1bQQEs-0003xA-1d TLS error on connection to xx.xxx.com
[148.251.254.194] (send): The specified session has been invalidated for
some reason.
2016-07-22 08:01:25 1bQQEs-0003xA-1d ** xx@??? R=dnslookup
T=remote_smtp X=TLS1.2:ECDHE_RSA_AES_128_GCM_SHA256:128
DN="CN=xx.xxx.com,EMAIL=x@???": SMTP error from remote mail server
after MAIL FROM:<bijuan@???> SIZE=8160: host xx.xxx.com
[x.y.z.194]: 550 Access denied - Invalid HELO name (See RFC2821 4.1.1.1)
++++++++++++ Log End ++++++++++++++++++++++++++

I also have this log:
++++++++++++ Log Start ++++++++++++++++++++++++++
mail:/etc/exim4# swaks -a -tls -q HELO -s mail.rajagiritech.ac.in -au
bijuan -ap '<>'
=== Trying mail.rajagiritech.ac.in:25...
=== Connected to mail.rajagiritech.ac.in.
<- 220 mail ESMTP Exim 4.84_2 Fri, 22 Jul 2016 19:03:35 +0530
-> EHLO mail.rajagiritech.ac.in
<- 250-mail Hello mail.rajagiritech.ac.in [192.168.0.241]
<- 250-SIZE 52428800
<- 250-8BITMIME
<- 250-PIPELINING
<- 250-STARTTLS
<- 250 HELP
-> STARTTLS
<- 220 TLS go ahead
=== TLS started with cipher TLSv1.2:ECDHE-RSA-AES256-GCM-SHA384:256
=== TLS no local certificate set
=== TLS peer DN="/C=IN/O=rset/CN=mail.rajagiritech.ac.in"
~> EHLO mail.rajagiritech.ac.in
<~ 250-mail Hello mail.rajagiritech.ac.in [192.168.0.241]
<~ 250-SIZE 52428800
<~ 250-8BITMIME
<~ 250-PIPELINING
<~ 250 HELP
~> QUIT
<~ 221 mail closing connection
=== Connection closed with remote host.
++++++++++++ Log End ++++++++++++++++++++++++++

Because of this, mails are not going to certain domains.

Can anyone tell me what is the issue and how to solve this?

Regards,
Biju.