A) \[2n\pi \pm \frac{\pi }{6}\]
B) \[n\pi +\frac{\pi }{6}\]
C) \[n\pi +{{(-1)}^{n}}\frac{\pi }{6}\]
D) \[n\pi +{{(-1)}^{n}}\frac{5\pi }{6}\]
Correct Answer: C
Solution :
[c] Middle term in the expansion is \[{{\left( \frac{10}{2}+1 \right)}^{th}}\] i.e., 6th tern. Thus \[{{T}_{6}}=7\frac{7}{8}\Rightarrow {{\,}^{10}}{{C}_{5}}\frac{1}{{{x}^{5}}}.{{x}^{5}}\,\,{{\sin }^{5}}x=\frac{63}{8}\] \[\Rightarrow 252.{{\sin }^{5}}x=\frac{63}{8}\Rightarrow {{\sin }^{5}}x=\frac{1}{32}\] \[\Rightarrow \sin x=\frac{1}{2}\] \[\therefore x=n\pi +{{(-1)}^{n}}\frac{\pi }{6}\]
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