JEE Previous Year Question

Let $\text{x}$ denote the fractional part of $x$ and $f\text{(}x\text{)}=\frac{{\text{cos}}^{-1}\text{⁡}(1-{\text{x}}^2){\text{sin}}^{-1}\text{⁡}\text{(}1-\text{x}\text{)}}{\text{x}-{\text{x}}^3}\text{,}x\ne 0$. If $L$ and $R$ respectively denotes the left hand limit and the right hand limit of $f\text{(}x\text{)}$ at $x=0$, then $\frac{32}{{\pi }^2}(L^2+R^2)$ is equal to

Topic: JEE PYQ

Answer: 18. Full step-by-step solution below.