The number of molecules/ions that show linear geometry among the following is _____. SO₂, BeCl₂, CO₂, N₃⁻, NO₂, F₂O, XeF₂, NO₂⁺, I₃⁻, O₃
To determine the number of molecules/ions that exhibit linear geometry, we need to analyze each species and determine its molecular geometry based on the VSEPR (Valence Shell Electron Pair Repulsion) theory. The configurations for these molecules/ions are analyzed as follows:
Count of linear geometry species: BeCl₂, CO₂, N₃⁻, XeF₂, NO₂⁺, I₃⁻; totaling to 6.
The calculated number correctly falls within the provided solution range of 6 to 6.
Total number of linear molecules/ions: 6
If the mean and the variance of 6, 4, a, 8, b, 12, 10, 13 are 9 and 9.25 respectively, then \(a + b + ab\) is equal to:
Given three identical bags each containing 10 balls, whose colours are as follows:
| Bag I | 3 Red | 2 Blue | 5 Green |
| Bag II | 4 Red | 3 Blue | 3 Green |
| Bag III | 5 Red | 1 Blue | 4 Green |
A person chooses a bag at random and takes out a ball. If the ball is Red, the probability that it is from Bag I is $ p $ and if the ball is Green, the probability that it is from Bag III is $ q $, then the value of $ \frac{1}{p} + \frac{1}{q} $ is:
If \( \theta \in \left[ -\frac{7\pi}{6}, \frac{4\pi}{3} \right] \), then the number of solutions of \[ \sqrt{3} \csc^2 \theta - 2(\sqrt{3} - 1)\csc \theta - 4 = 0 \] is equal to ______.