I'm looking for a method that is support my HTML5 quiz game and I'm a fresher for game programming. I would like to know if it is the best Free HTML5 Engine that suits with a multiplayer quiz game? it also should handle servers and the questions should be stored in a database.
Sounds like you should check out Construct2.
Best HTML5 engine out there imo. 2D anyways.
If you have the game assets you could make that quiz in 2 hours.
That being said, I don't know of anything that more directly supports your needs, although you could consider a combination of node.js for server side logic, nowjs to simplify communication between your server and client-side, and any library you're comfortable with for the front-end -- some popular choices include LimeJS, Impact, melonJS, and Crafty -- or as mentioned above you could use Construct 2's plug-in SDK to connect to your server-side logic.
You said you're "a fresher" to programming, but do you have any experience or are you starting completely from scratch?
I think for a quiz, maybe Jquery. I haven't used it, just seen posts about it. I don't think you need html5 so much as Ajax, so you don't have to do a complete page refresh after a post. Not really a web guy, though.
As far as html5 game engines, I think Impact looks really good, but costs 100 dollars. EaselJS also looks good and is open source.