When I click "Next" it shows next page but some questions are same with previous page's questions. For Example in previous page I see some question then I click next and see same question again.
This isn't a bug - the system is doing exactly what you ask, which is giving you questions 16-30 in the current list. "The current list" is a different list pretty much every time you ask for it, of course, but that doesn't change what you asked for.
What you may be interested in is the answer to this question: RSS feed of your favorite tags. If you want to see new questions but only ever see a question once, the RSS 'news' model seems more appropriate than paginated a constantly-changing list.
See if it does what you want.
Per screen shot it looks like you use default setting to display 15 questions per page. Per my recollection, "reappearing questions" were indeed a noticeable annoyance with this setting.
To me, the annoyance has gone when I changed settings to display 50 questions per page:
Not that above change magically fixed Next page - quite opposite, there are typically more of reappearing questions shown at 50-per-page setting. But somehow, difficult to tell why, just somehow this doesn't feel wrong anymore.
Maybe this is because with 50-per-page setting I spend much more time browsing first page questions so that seeing "reappearing questions" after I click Next feels justified.
Page numbers is not important I want to see only new questions. I expect only this function from "next button". There must be solution for such problems in dynamic content sites.
Sure there is a solution. For the case of SO though I doubt that it is worth implementing. Thing is what you want involves certain complication of UI. Just think of it...
Would you expect just showing a second page as it would have been few hours ago? Would that feel right taking into account that as of now, this would be 22nd page not 2nd (remember hundred or something of new questions appearing while first page hangs)?
Question lists are cached for two minutes for all users - it's not really feasible for us to store which questions each user has seen during their session.
The other answers give good work-arounds for this intended behavior.