For product formation from only one type of reactant (e.g. A \(\rightarrow\) product), the CORRECT match for the order of the reaction (given in Column I) with the half-life expression (given in Column II) is:
(\([A]_0 \) is the initial concentration and \( k_r \) is the rate constant)
For the reaction $ A \rightarrow $ products,
The reaction was started with 2.5 mol L\(^{-1}\) of A.
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: