Al2O3
Tl2O3
Ga2O3
B2O3
As we move down Group 13, the metallic character increases, and hence the electropositive character increases. As electropositivity increases, the basicity of the oxides increases.
The order of basicity for Group 13 oxides is \( \text{B}_2\text{O}_3 < \text{Al}_2\text{O}_3 < \text{Ga}_2\text{O}_3 < \text{In}_2\text{O}_3 < \text{Tl}_2\text{O}_3 \).
\( \text{Tl}_2\text{O}_3 \) is the most basic oxide.
Let A be a 3 × 3 matrix such that \(\text{det}(A) = 5\). If \(\text{det}(3 \, \text{adj}(2A)) = 2^{\alpha \cdot 3^{\beta} \cdot 5^{\gamma}}\), then \( (\alpha + \beta + \gamma) \) is equal to:
Let \( \alpha, \beta \) be the roots of the equation \( x^2 - ax - b = 0 \) with \( \text{Im}(\alpha) < \text{Im}(\beta) \). Let \( P_n = \alpha^n - \beta^n \). If \[ P_3 = -5\sqrt{7}, \quad P_4 = -3\sqrt{7}, \quad P_5 = 11\sqrt{7}, \quad P_6 = 45\sqrt{7}, \] then \( |\alpha^4 + \beta^4| \) is equal to: