$\begin{array}{1 1}(A)\;0^{\circ} \\(B)\;\pi/4 \\(C)\;\pi/2 \\(D)\;\pi \end{array} $

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Since $\overrightarrow{P} \times \overrightarrow{Q}$ is a vector normal to the plane containing the vectors $\overrightarrow{P}$ and $\overrightarrow{Q}$ and $(\overrightarrow{P}+\overrightarrow{Q})$ lies in the same plane, the angle between $\overrightarrow{P} \times \overrightarrow{Q}$ and $\overrightarrow{P}+\overrightarrow{Q}$ is $90^{\circ}$

Hence C is the correct answer.

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