Sum of \(\pi\)-bonds present in peroxodisulphuric acid and pyrosulphuric acid is___________
Count π-bonds in double bonds (C=O, S=O, etc.) while analyzing structures of acids.
• Peroxodisulphuric acid: Structure: \[ H - O - S(=O)_2 - O - O - S(=O)_2 - O - H \] Number of \(\pi\)-bonds = 4 (two in each \(\text{SO}_3\) group)
• Pyrosulphuric acid: Structure: \[ H - O - S(=O)_2 - O - S(=O)_2 - O - H \] Number of \(\pi\)-bonds = 4 (two in each \(\text{SO}_3\) group).
Total \(\pi\)-bonds = \(4 + 4 = 8\).
Given below are two statements.
In the light of the above statements, choose the correct answer from the options given below:
If $ \lim_{x \to 0} \left( \frac{\tan x}{x} \right)^{\frac{1}{x^2}} = p $, then $ 96 \log_e p $ is equal to _______
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: