dear all,
any one to assist on appropriate way of partitioning ubuntu 14.0. server?

most needed partitions and their size for application server.

There is no one answer to that question, not as it was presented.

What kind of server are you building? What services will it provide? What kind of network environment have you to deal with? Are there local or corporate standards that constrain your options?

Generally, you want a small space for boot (.5G), some space for root and /usr (10G? 20G? depending), a few gig for /var, and how much depend upon what spooling you plan (mail, printing, etc.), possibly some space for /home - depending upon what home folders will be allowed, possibly /opt if you will install something that uses enough of it to be worth the effort, and some special space for data or segregated applications (/vz for openvz, /data for most databases, /oracle for that one, there are as many options here as major application suites).

I try to keep it simple (/boot, /, /var /data, and swap are my most common choices) but it must be complete enough to protect your system. (/var, for example, not on root protects from a spooler overflow from crashing your machine.)

Really, if you want a clear and targeted answer you must give us a clear target to shoot at! ;-)