I am doing a project on compareing different linux distributions' purposes. These distributions include:

1 Yoper
2 Redhat 9.0
3 Mandrake 9.1
4 Slackware 9.1
5 SuSE 8.2
6 Debian

I need to find out their suitablity for different purproses such as: software development, server, multimedia, home use and office use. Can anyone tell me the best solution for these purproses? thank you.

I would say any of them will work for that, it really depends on your personal likings. So you will need to decide for yourself.

Since it's going to be a server (of some kind) or be on a network or Internet I would try RedHat, mainly due to the up2date feature. It is a lot of work to keep track of all bugs and vunerabilities on your own. Up2date will do it for you.

I have tried Mandrake and the update program needed some mojor work, maybe it's better now.

Don't know about SuSE or Debian, never heard of Yoper.

Please do not double post in the future. It causes confusion.

I can tell you a bit about SuSE :
YOU (Yast Online Update) is quite a user-friendly tool for keeping your system "up-to-date" , if that's the proper phrase for it ; Keep in mind ,that most "Update-services" are seriously lagging when it comes to keeping up with the software-development.
If you're depending on the provided default services , you'll be stuck with a "Neolithic" system. It's safe and stable , but don't expect to be "bleeding edge".
After all ; the software and patches , provided by those update-services , are prone to rigourous testing and checking. That takes time and so it can't be helped that most of it will be outdated by the time it makes it to the service.

This holds true for (nearly?) every major distro.(But I have to say ; SuSE is about the slowest in this regard. At least , in my experience)

Redhat: Nothing special, main purpose to have a distro suitable for everyone, newbie to expert. didn't like it.
SUSE: never tried, sorry.
Mandrake: Newbie distro, to ms-like for me...
Slackware: a development distro, includes many dev packages
Debian: suitable for everything, you can make of it anything you want. not too good for beginners.
Gentoo: Do it yourself distro, for the ones who are afraid of lfs
Arch: My distro, an expert distro optimized for i686, mainly in development...