Does a 7 inch tablet use greater RAM for a task than a 4 inch phone for same task with other specs constant? Does screen size affect RAM usage?
Based on your question and the answers given, I assume you are asking about the resources consumed to display the Android environment on a tablet compared to a phone. If the number of pixels in each display is equal, then the resources used will be the same...
HOWEVER, the phone will always use more resources due to it's communications with a cell tower.
Yes. It takes more ram to fill a larger display. Every time.
The only difference will be in graphical rendering. If you were to play Angry Birds, the game itself would take the same amount of Ram as your phone + the extra Ram needed for the extra rendering on the larger screen.
even playing video on bigger screen needs more ram, if you check nexus 10 ram you will see it has 2 more time ram than nexus 7, so basically on both screens applications, videos should perform the same (i guess!). Only when you get ram saturation you will see the benefit of having more ram thus bigger screen since it has more ram or smaller screen with more ram.
Techically, yes, but the difference will usually be marginal. Since every pixel on the screen is "mapped" onto a memory location, the screen itself will require more memory, and if the contents are graphics-intensive, more memory may be required by the system in preparing the image. However, in practice this equates to a handful of megabytes of RAM (depending on the exact resolution), so it won't make much difference to the performance of the phone.
asked if other factors like - graphics-intensivity , screen resolution are constant
I understand, but the answer is different for different types of graphics intensity! For "non-graphic" apps (e.g. Mail), the answer is that the difference will be minimal (=the difference between the resolutions x no. of bits per pixel). For high intensity graphics (particularly games with high graphic content), it may make a significant difference.