List of top Statistics Questions on Mean value theorems

X+2Y=5 and 2X+3Y=8. Find the Mean of X and Y.
Let \( \mathcal{F} = \{ f: [a, b] \to \mathbb{R} \mid f \text{ is continuous on } [a, b] \text{ and differentiable on } (a, b) \} \).
Which one of the following options is correct?