Q .     Let `f(x)=x^{2}` and `g(x)=\sin x` for all `x\in \mathbb{R}`. Then the set of all `x` satisfying `(f\circ g\circ g\circ f)(x)=(g\circ g\circ f)(x)` , where `(f\circ g)(x)=f(g(x))` , is

JEE 2011 ADVANCED Paper - 2
A

`\pm\sqrt{n\pi},\ n\in\{0,1,2,\ldots\}`

B

`\pm\sqrt{n\pi},\ n\in\{1,2,\ldots\}`

C

`\frac{\pi}{2}+2n\pi , n\in\{\ldots,\ -2,\ -1,0,1,2,\ \ldots\}`

D

`2 n\pi,\ n\in\{\ldots,\ -2,\ -1,0,1,2,\ \ldots\}`

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