I have the following battery.
3 cell Lithium Polymer rechargeable battery. It is rated at 11.1V, 1800mAh. It can give discharge current up to 36Amps (20C discharge).

My question is whether can i use it with 2212/10 motor whose operating current is between 2-6Amp.

The peak current for that motor seems to be 16A, so use a 20A ESC and try an 8x4 or 8x5 prop (there are some other safe prop choices also).  

That battery should work fine, as long as the AUW of the model is close to 500 grams (not much higher than 600grams to be safe).

Anwar Sir,

Actually I came across the battery at  Nex Robotics (http://www.nex-robotics.com/products/batteries-and-chargers/lithium-polymer-3cell-11.1v-1800mah-20c-discharge-battery.html) Which costs around Rs.877.5/-. which i think is very cheap.

Can we use this battery in models.

As I mentioned in my above post, it should work, as long as your total model weight (including the battery) is not much above 500 to 600 grams.

You should also read the posts in the RC India Gems about how important the combination of Motor, ESC and Prop are along with the battery for your electrical setup to work right.  Just choosing the right battery alone is not enough !