If the middle term of \( \left(x+\frac{1}{x} \sin ^{-1} x\right)^{8...

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If the middle term of \( \left(x+\frac{1}{x} \sin ^{-1} x\right)^{8} \) is \( \frac{35 \pi^{4}}{8} \), then value of \( x \) can be
(a) \( 1 / 2 \)
(b) \( \sqrt{3} / 2 \)
(c) \( 1 / \sqrt{2} \)
(d) 1
\( \mathrm{P} \)
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