Chọn: Đáp án C

Phương trình có chùm mặt phẳng (P) chứa Oz là $mx+ny=0$

Vậy (P) có PVT $\overrightarrow{u}=\left( m,n,0 \right)$

$\left( \alpha  \right)$ có PVT $\overrightarrow{v}=\left( 2,1,-\sqrt{5} \right)$

Ta có $\cos \left( \left( P \right),\left( \alpha  \right) \right)=\left| \cos \left( \overrightarrow{u,}\overrightarrow{v} \right) \right|=\frac{\left| 2m+n \right|}{\sqrt{{{m}^{2}}+{{n}^{2}}}\sqrt{4+1+5}}=\cos {{60}^{0}}=\frac{1}{2}$

$\Leftrightarrow \frac{\left| 2m+n \right|}{\sqrt{10.}\sqrt{{{m}^{2}}+{{n}^{2}}}}=\frac{1}{2}\Leftrightarrow 2\left| 2m+n \right|=\sqrt{10}.\sqrt{{{m}^{2}}+{{n}^{2}}}$

$\Leftrightarrow 16{{m}^{2}}+16mn+4{{n}^{2}}=10{{m}^{2}}+10{{n}^{2}}\Leftrightarrow 6{{m}^{2}}+16mn-6{{n}^{2}}=0$

Cho $n=1\Rightarrow 6{{m}^{2}}+16m-6=0\Leftrightarrow \left[ \begin{align}  & {{m}_{1}}=\frac{1}{3} \\  & {{m}_{2}}=3 \\ \end{align} \right.$

Vậy ta có 2 mặt phẳng (P) là

$\left( {{P}_{1}} \right):-3x+y=0;\left( {{P}_{2}} \right):\frac{1}{3}x+y=0\Leftrightarrow x+3y=0$