Step 1: Understanding the coagulation process
Blood exists as a negatively charged sol. When ferric chloride (FeCl$_3$) is introduced, the Fe$^{3+}$ ions interact with the negatively charged blood sol, causing it to coagulate. This occurs due to the electrostatic attraction between the positively charged Fe$^{3+}$ ions and the negatively charged blood particles.
Step 2: The role of \(Fe^{3+} ions\)
The Fe$^{3+}$ ions neutralize the negative charge on the blood particles, leading to their aggregation and coagulation. This explains why Fe$^{3+}$ ions are responsible for facilitating the coagulation of blood.
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: