We know x and y are prime numbers greater than 10 , so x and y must be odd (The only even prime number is 2 ). We need to check that which of the given options represents an even integer.

(A) $\(x^2+x y=x(x+y)=odd \times (odd + odd )= odd \times even =even$\)

(B) $\(x^y+2=odd ^{odd} +2=odd +2= odd\)$

(C) $\(x y+2=odd \times odd +2= odd +2=odd\)$

(D) $\(2 x y+x y=3 x y=3 \times odd \times odd =odd\)$

(E) $\(2 x+3 y=2 \times odd +3 \times odd=even + odd =odd\)$

Hence the answer is $\((\mathrm{A})\)$.