CSIR NET Maths previous year question papers

Let $\mu$ denote the Lebesgue measure on $\mathbb{R}$ and $f : \mathbb{R} \to [0, \infty)$ be a Lebesgue measurable function. For n ≥ 1, let $E_{n} =$ {$x \in \mathbb{R} : n - 1 \le f(x) < n$}. Suppose that $\sum(n\ge1) n^{2}\mu(E_{n}) < \infty$. Which of the following statements are true?