I have more categories and subcategories in my site but problem category backend page is not opened . please provide the solution and exact server configration to manage the category .
Wow, that's a vague problem which you've described and you're asking for an exact solution. I'm sorry, but nobody is capable of providing you exacts until we know more.
Enable Logging in Magento and make sure that PHP Error logging is enabled on your webserver. Attempt to open the backend category management a few times and then go open your error logs. Paste your error here and then I can begin to narrow down on the problem.