Q64 / 180 · KCET 2025 · Mathematics

If $f(x)=\sin \left[\pi^2\right] x-\sin \left[-\pi^2\right] x$, where $[x]=$ greatest integer $\leq x$, then which of the following is not true?

  • A
    $f(0)=0$
  • B
    $f\left(\frac{\pi}{2}\right)=1$
  • C
    $\mathrm{f}\left(\frac{\pi}{4}\right)=1+\frac{1}{\sqrt{2}}$
  • Correct answer
    D
    $f(\pi)=-1$

Solution

$\begin{aligned} & f(x)=\sin \left[\pi^2\right] x-\sin \left[-\pi^2\right] x \\ & =\sin 9 x-\sin (-10) x \\ & =\sin 9 x+\sin 10 x \\ & f(\pi)=\sin 9 \pi+\sin 10 \pi=0\end{aligned}$

Hence, the correct answer is option: 'D'.

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