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Q.

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

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a

2nπ+π6,n∈z

b

nπ+π6,n∈z

c

nπ+−1nπ6,n∈z

d

nπ+−1nπ3,n∈z

answer is C.

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Detailed Solution

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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