We can manually upgrade  the Cpanel latest version using cpanel scripts the name of upcp its being under the directory /scripts/,

Login into your server with SSH and check the cpanel version,

[root@cpanel ~] #  /usr/local/cpanel/cpanel -V

11.34.2 (build 8)

To update latest version execute the  upcp script,
[root@cpanel ~]#  /scripts/upcp --force

Once it will be upgraded latest version take a backup of exim few important files by cp or rsync command,
 [~]# rsync /etc/exim.conf /etc/exim.conf-`date +%F`
 [~]# rsync /etc/exim.conf.local /etc/exim.conf.local-`date +%F`
 [~]# rsync /etc/exim.pl /etc/exim.pl-`date +%F`
 [~]# rsync -r /etc/mail/spamassassin /etc/mail/spamassassin-`date +%F`
 [~]# rsync -r /usr/local/cpanel/etc/exim /usr/local/cpanel/etc/exim-`date +%F`
 [~]# rsync -r /etc/exim /etc/exim-`date +%F`

Run the following script to rebuild the exim configuration,
 [~]# /scripts/buildeximconf

After completed this process check the latest version of Cpanel,
 [~]# /usr/local/cpanel/cpanel -V

11.40.1 (build 11)