If the middle term of $$1x+xsin$$⁡$$x10$$ is equal to $$778$$ , then the value of x is

Correct option is 3nπ+−1nπ6,n∈z

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

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2nπ+π6,n∈z

nπ+π6,n∈z

nπ+−1nπ6,n∈z

nπ+−1nπ3,n∈z

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detailed solution

Correct option is C

1x+xsin⁡x10 n=10 is even M. T=T102+1=T5+1=778⇒10c51x5(xsin⁡x)5=638⇒10×9×8×7×65×4×3×2×11x5x5sin5⁡x=638⇒63×4sin5⁡x=638⇒sin5⁡x=132⇒sin⁡x=12⇒x=nπ+(−1)nπ6,n∈z

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If the middle term of 1x+xsin⁡x10 is equal to 778 , then the value of x is

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