$[\text{Cr(H}_2\text{O)}_6]^{3+} \text{ contains } \text{Cr}^{3+}: [\text{Ar}]3d^3 \cdot t_{2g}^3 e_g^0$
$[\text{Fe(H}_2\text{O)}_6]^{3+} \text{ contains } \text{Fe}^{3+}: [\text{Ar}]3d^5 \cdot t_{2g}^3 e_g^2$
$[\text{Ni(H}_2\text{O)}_6]^{2+} \text{ contains } \text{Ni}^{2+}: [\text{Ar}]3d^8 \cdot t_{2g}^6 e_g^2$
$[\text{V(H}_2\text{O)}_6]^{3+} \text{ contains } \text{V}^{3+}: [\text{Ar}]3d^2 \cdot t_{2g}^2 e_g^0$
Let one focus of the hyperbola $ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 $ be at $ (\sqrt{10}, 0) $, and the corresponding directrix be $ x = \frac{\sqrt{10}}{2} $. If $ e $ and $ l $ are the eccentricity and the latus rectum respectively, then $ 9(e^2 + l) $ is equal to:
The largest $ n \in \mathbb{N} $ such that $ 3^n $ divides 50! is: