There are many ways for figuring out if you have a DirectX11 card, so here are the approaches that you can use, with a bonus right at the end of the post.
Run DxDiag
WindowsKey + R, type DxDiag and hit Enter. That is the DirectX diagnostic tool, which unfortunately, only tells you on the "System" tab what is the highest version of DirectX installed on your machine. So if it reports DirectX 11, that doesn't mean you have a DX11 driver! The "Display" tab has a promising "DDI version" label, but unfortunately that doesn't seem to be accurate on the machines I've tested it with (or I may be misinterpreting its use). Either way, this tool is not the one you want for this purpose, although it is good for telling you the WDDM version among other things.
Use the Microsoft hardware page
There is a Microsoft Windows 7 compatibility center, that lists all hardware (tip: use the advanced search) and you could try and locate your device there… good luck.
Use Wikipedia or the hardware vendor's website
Use the Wikipedia page for the vendor cards, for both nvidia and amd. Often this information will also be in the specifications for the cards on the IHV site, but is is nice that wikipedia has a single page per vendor that you can search etc. There is a column in the tables for API support where you can see the DirectX version.
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