In the trivalent state, most of the compounds are covalent and are hydrolyzed in water. Trichlorides, upon hydrolysis in water, form tetrahedral \([\text{M(OH)}_4]^-\) species, and the hybridization state of element M is \( sp^3 \).
In the case of aluminum, acidified aqueous solution forms octahedral \([\text{Al(H}_2\text{O)}_6]^{3+}\) ion.
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: