List of top Mathematics Questions on Mean Value Theorem asked in BITSAT

The value of c∈(0,2) satisfying the mean value theorem for the function f(x)=x(x-1)² on [0,2] is:
If \( f(x) = x^\alpha \log x \) and \( f(0) = 0 \), then the value of \( \alpha \) for which Rolle's theorem can be applied in \( [0, 1] \) is: