what is the file system used in linux os and what r the ways creating file
systems and their management.what is the purpose of mount and unmount commands.

Although you can find the answer of this questions using a search engine
I will give you very short answer
File systems ext2 , erxt3, ext4
mount and umount linux files can be on different partitions or drives.
To read or write on this files you use the command mount when when ready umount see also man mount and man umount

Per the LQ Rules, please do not post homework assignments verbatim. We're happy to assist if you have specific questions or have hit a stumbling point, however. Let us know what you've already tried and what references you have used (including class notes, books, and Google searches) and we'll do our best to help. Also, keep in mind that your instructor might also be an LQ member.

There are many; just a few have already been mentioned, but, just to give you a little practice in what is obviously a homework assignment, trying wikipedia for a comparison of filesystems will give you more information than you need.

'text-ese' is not approved of here. There are several programs that can create file systems; is 'with a program' the kind of answer that you were looking for? If it isn't, I don't know what you are asking.

hmm, the management of file systems; do you mean 'checking whether they are getting too full' in which case there are generic Linux/Unix tools which are applicable; do you mean things like checking for bad blocks and correcting data and metadata errors; in which case there are different tools for diferent filesystem types, but they all (AFAIK; I don't know for some of the more obscure FS types, but I assume that they are the same) are some kind of file system check tool named after an abbreviation of the purpose of the tool, usually concatenated with the name of the filesystem type to which they are applicable. Anyone practised with 'man -k' (or 'apropos') will easily be able to discover more.

'Mount' mounts file systems (makes them available); the messy details are available in the man page and unmount, as a command, does not exist. I think you mean umount and by now you ought to be able to guess where the details are available and the overall purpose of the command. If not, please post again and we can all be amazed how little of this you can do by yourself.

The question that you didn't ask is why the system should need to mount and unmount disks.