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

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2nπ+π6

nπ+πc

nπ+(−1)nπ6

nπ+(−1)nπ3

answer is C.

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Detailed Solution

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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