if I type any keyword, I want to get the list of asked questions which has match keyword from all the group/forum/blog in the search result.
So you just want to search, but filter it to questions? That should be a matter of using filtering.
I'd recommend reviewing community.telligent.com/.../search-filters-and-facets
Are you trying to develop a widget? The advanced search widget already supports this scenario with its facet options it shows in the right sidebar. As that widget supports a lot more than just basic searching, its implementation is fairly complex as a starting point for learning about widget development, but it does potentially meet your requirement already.