Alkaline oxidative fusion of \(MnO_2\) gives “A” which on electrolytic oxidation in alkaline solution produces B. A and B respectively are:
The process described involves the oxidative reactions of manganese compounds in alkaline solutions.
Alkaline Oxidative Fusion of \(MnO_2\): When \(MnO_2\) is subjected to oxidative fusion in an alkaline medium, it can form \(MnO_4^{2-}\) (manganate ion) under alkaline conditions. The reaction can be represented as:
\(2MnO_2 + 2OH^- + O_2 \rightarrow 2MnO_4^{2-} + H_2O\).
Electrolytic Oxidation of Product A: The product A formed from the oxidative fusion of \(MnO_2\) can be oxidized electrolytically in alkaline solution to form \(MnO_4^-\) (permanganate ion). The overall reaction is:
\(MnO_2 + 2e^- \rightarrow MnO_4^-\).
Thus, the products A and B formed in the given reaction sequence are: A = \(MnO_4^{2-}\) and B = \(MnO_4^-\).
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:
Let $ P_n = \alpha^n + \beta^n $, $ n \in \mathbb{N} $. If $ P_{10} = 123,\ P_9 = 76,\ P_8 = 47 $ and $ P_1 = 1 $, then the quadratic equation having roots $ \alpha $ and $ \frac{1}{\beta} $ is: