Let R be a region in the first quadrant of the xy plane enclosed by a closed curve C considered in counter-clockwise direction. Which of the following expressions does not represent the area of the region R?

Let $$\,{y^2} - 2y + 1 = x$$ and $$\,\sqrt x + y = 5.\,\,$$ The value of $$\,x + \sqrt y \,\,$$ equals ________. (Given the answer up to three decimal places)

Consider a function $$f\left( {x,y,z} \right)$$ given by $$f\left( {x,y,z} \right) = \left( {{x^2} + {y^2} - 2{z^2}} \right)\left( {{y^2} + {z^2}} \right).$$ The partial derivative of this function with respect to $$x$$ at the point $$x=2, y=1$$ and $$z=3$$ is _______.

Let $$x$$ and $$y$$ be integers satisfying the following equations $$$2{x^2} + {y^2} = 34$$$ $$$x + 2y = 11$$$
The value of $$(x+y)$$ is _________.