\[ \begin{array}{|c|c|} \hline \textbf{LIST-I (Redox Reaction)} & \textbf{LIST-II (Type of Redox Reaction)} \\ \hline A. \, CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(l) & I. \, \text{Disproportionation reaction} \\ B. \, 2NaH(s) \rightarrow 2Na(s) + H_2(g) & II. \, \text{Combination reaction} \\ C. \, V_2O_5(s) + 5Ca(s) \rightarrow 2V(s) + 5CaO(s) & III. \, \text{Decomposition reaction} \\ D. \, 2H_2O(aq) \rightarrow 2H_2(g) + O_2(g) & IV. \, \text{Displacement reaction} \\ \hline \end{array} \]
Step 1: The reaction \( CH_4 + O_2 \) is a combination reaction (A-II).
Step 2: The reaction \( 2NaH \rightarrow 2Na + H_2 \) is a decomposition reaction (B-III).
Step 3: The reaction \( V_2O_5 + Ca \) is a redox displacement reaction (C-I).
Step 4: The reaction \( 2H_2O \rightarrow 2H_2 + O_2 \) is a displacement reaction (D-IV).
Final Conclusion: The correct matching is Option (3), A-II, B-III, C-I, D-IV.
200 cc of $x \times 10^{-3}$ M potassium dichromate is required to oxidise 750 cc of 0.6 M Mohr's salt solution in acidic medium. Here x = ______ .

Let \( \alpha = \dfrac{-1 + i\sqrt{3}}{2} \) and \( \beta = \dfrac{-1 - i\sqrt{3}}{2} \), where \( i = \sqrt{-1} \). If
\[ (7 - 7\alpha + 9\beta)^{20} + (9 + 7\alpha - 7\beta)^{20} + (-7 + 9\alpha + 7\beta)^{20} + (14 + 7\alpha + 7\beta)^{20} = m^{10}, \] then the value of \( m \) is ___________.