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Question Id : 17920 | Context : JEE Main 2026 (21 January Evening Shift)
If the area of the region ${(x,y) : 1 - 2x \le y \le 4 - x^2,; x \ge 0,; y \ge 0}$ is $\frac{\alpha}{\beta}$, $\alpha, \beta \in \mathbb{N}$, $\gcd(\alpha,\beta) = 1$, then the value of $(\alpha + \beta)$ is:

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