Don't worry about 720p or 1080p. They are broadcasting standard and don't have a lot to do with actual screen size, and either resolution will display on your screen.
Refer your screen res to the actual number of horizontal and vertical pixels (1366x768, 1440x900, 1920x1080, etc)
i want to play games with this monitor thats why im asking..my max res is 1600x900 if i set in this resolution and play the game what it is 900p or 720p or 1080p
Still a better idea to write out the full res (1600x900) because not everyone knows the name of the corresponding resolution and if you say 900p, it refers to the number of vertical lines, so it could be (1440x900, 16:10) or (1200x900, 4:3) as well.
As great as this answer is; and I should add that I refer to the resolution image on that Wikipedia page all the time; the irony for me, is that the reason I landed on this page and found this answer was precisely because the Wikipedia page and the image of resolutions it shows DOES NOT actually include the 1600 x 900 resolution on it.
So while the suggestion to refer to that page and image is extremely useful and helpful in the general sense of showing the various monitor resolutions and provides an instant reference to compare sizes, it does not actually help provide any information about 1600 x 900 resolution. For me, I was looking to see if that resolution has a standard name, and all I've been able to find is that it is "generally" referred to as HD+, but doesn't appear to have a standards-organization designation, which I find insanely frustrating.
I don't want to knock your answer too hard, because it really is helpful in the general sense; it just doesn't actually answer the question at hand.