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RELATIONS AND FUNCTIONS — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSRELATIONS AND FUNCTIONS1 Mark
MCQ
If $\text{f(x)}=\sin[\pi^2]\text{x}+\sin[-\pi^2]\text{x},$ where [x] denotes the greatest integer less than or equal to x, then:
  • ✓
    $\text{f}\Big(\frac{\pi}{2}\Big)=1$
  • B
    $\text{f}(\pi)=2$
  • C
    $\text{f}\Big(\frac{\pi}{4}\Big)=-1$
  • D
    None of these.
✓

Answer

Correct option: A.
$\text{f}\Big(\frac{\pi}{2}\Big)=1$
$\text{f(x)}=\sin[\pi^2]\text{x}+\sin[-\pi^2]\text{x}$
$\Rightarrow\text{f(x)}=\sin\big[9.8\big]\text{x}+\sin\big[-9.8\big]\text{x}$
$\Rightarrow\text{f(x)}=\sin9\text{x}-\sin10\text{x}$
$\Rightarrow\text{f}\Big(\frac{\pi}{2}\Big)=\sin9\times\frac{\pi}{2}-\sin10\times\frac{\pi}{2}$
$\Rightarrow\text{f}\Big(\frac{\pi}{2}\Big)=1-0=1$

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