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Question Id : 18056 | Context : JEE Main 2026 (24 January Morning Shift)
Let a differentiable function $f$ satisfy the equation $\int_0^{36} f\left(\frac{tx}{36}\right)dt=4\alpha f(x)$ If $y=f(x)$ is a standard parabola passing through the points $(2,1)$ and $(-4,\beta)$, then $\beta^\alpha$ is equal to ______.


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