The area of bounded region R defined as \( R = \{(x,y): 0 < x < 2,\; 1 < y < 3,\; y > x \} \) is
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: