$11 \cdot 1$ In the expansion of $\left(\frac{x^{2}}{2}-\frac{2}{x}\right)^{8}$, the coefficient of $x^{7}$ is
(A) 56 .
(B) -56 .
(C) 14 .
(D) -14 .
(E) 0 .
(11th American High School Mathematics Examination, 1960)
[Solution] From $\left(\frac{x^{2}}{2}-\frac{2}{x}\right)^{8}=\frac{1}{(2 x)^{8}}\left(x^{3}-4\right)^{8}$, thus, we only need to find the coefficient of $x^{15}$ in $\left(x^{3}-4\right)^{8}$, which is
$$
C_{8}^{5}\left(1^{3}\right)^{5}(-4)^{3}=-2^{6} C_{8}^{5},
$$

Therefore, the coefficient of $x^{7}$ in the expansion is $\frac{1}{2^{8}} \cdot\left(-2^{6} C_{8}^{5}\right)=-14$. Hence, the answer is $(D)$.