So I logged into the account, and enterd a keyword which is highly competitive. The result said that the keyword which I have entered is not been triggered by Google anymore because the keyword is not inserted or the keyword is paused or it has been deleted etc.
I checked the keyword in my ad campaign and it was very well there. So I manually checked the search results page and found out that my ad was been displayed on the fifth page.
Whereas for the other account(for different industry) I checked another keyword and the results showed that the ad is been displayed.
The difference between the two search was that in the first case the ad was displayed on the fifth page(since it's very competitive) whereas for the other ad it was been displayed on the first page (because of less competition). I'm not sure whether the positioning has anything to do with the way the "AD Diagnostic Tool" outputs it's result.
However, for one adgroup, I still have a problem finding out why my ad doesn't show up. My ad just simply doesn't show up for that particular widget in that particular adgroup. When I use the diagnostics tool, I get a list of all other adgroups and the reason why the particular widget does not show up the ads in those adgroups (the reason being low CTR), but that particular widget is not in the keyword list of all those other adgroups! The only one adgroup the widget is listed in, is not shown by the diagnostics tool.
Confusing...