If the middle term of $$1x+xsin$$⁡$$x10is$$ equal to $$778$$, then value of x is

Correct option is 3nπ+(−1)nπ6

Questions

If the middle term of ${(\frac{1}{x} + xsin x)}^{10}$ is equal to $7 \frac{7}{8},$ then value of x is

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2nπ+π6

nπ+πc

nπ+(−1)nπ6

nπ+(−1)nπ3

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detailed solution

Correct option is C

1x+xsin⁡x10Here, n=10 (even) ⇒ Middle term =102+1th=6thT6=10C51x10−5(xsin⁡x)5⇒ 252(sin⁡x)5=638⇒(sin⁡x)5=132⇒ sin⁡x=12⇒sin⁡x=sin⁡π/6∴ x=nπ+(−1)nπ6

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If the middle term of 1x+xsin⁡x10is equal to 778, then value of x is

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If the middle term of ${(\frac{1}{x} + xsin x)}^{10}$ is equal to $7 \frac{7}{8},$ then value of x is