MHTCET 16 Apr 2026 Shift 1 Paper

Concept:The function stays positive but approaches 0 without ever reaching it, so the minimum is not attained.Explanation:Let $f(x)=\frac{\log x}{x}$, where $x \in (2,\infty)$.For every finite $x>2$, we have $\log x>0$ and $x>0$.Therefore, $f(x)=\frac{\log x}{x}>0$ for all $x \in (2,\infty)$.Now consider the limit as $x$ becomes very large:$$\lim_{x \to \infty} \frac{\log x}{x}=0$$This shows the function can get arbitrarily close to 0, but it never actually equals 0 for any finite value of $x>2$.Thus, 0 is the infimum of the function, not the minimum value.Since the function never attains the value 0, the minimum does not exist in the given interval.Answer:Option D: Does not exist