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The number of solutions of the following...

The number of solutions of the following inequality `1/2^(sin^2 x_2)*1/3^(sin^2 x_2)*.....1/n^(sin^2 x_n) <= n !,` where `x_1 in(0,4 pi)` for `i-= 1,2,3,...,n,` is (i) `1` (ii)`4^(n-1)` (iii)` n^n` (iv) `infty`

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