Mathematics Question from JEE Main 2025 · 29 January, Shift 1

Let $[t]$ be the greatest integer less than or equal to $t$. Then the least value of $p \in \mathbb{N}$ for which $\lim_{x \to 0^{+}} \left( x \left( \left[ \frac{1}{x} \right] + \left[ \frac{2}{x} \right] + \cdots + \left[ \frac{p}{x} \right] \right) - x^2 \left( \left[ \frac{1^2}{x^2} \right] + \left[ \frac{2^2}{x^2} \right] + \cdots + \left[ \frac{9^2}{x^2} \right] \right) \right) \geq 1$ is equal to: