JEE Advance 2025 Paper 1

Let $\mathbb{R}$   denote the set of all real numbers. Define the function $f \colon \mathbb{R} \to \mathbb{R}$   by $f(x) = 2 - 2x^2 - x^2 \sin(1/x)$   if $x \neq 0$   and $f(0) = 2$  . Then which one of the following statements is TRUE?