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Consider the following statements:
\( S_{1} \) : Number of points where \( f(x)=\mid x \) sgn \( \left(1-x^{2}\right) \mid \) is non-differentiable is 3 .
P
\( \mathbf{s}_{2}: \quad \) Defined \( f(x)=\left[\begin{array}{ll}\operatorname{asin} \frac{\pi}{2}(x+1) & , x \leq 0 \\ \frac{\tan x-\sin x}{x^{3}}, & x0\end{array}\right. \) equal to \( \frac{1}{2} \)
\( \mathbf{S}_{3} \) : The set of all points, where the function \( \sqrt[3]{x^{2}|x|} \) is differentiable is \( (-\infty, 0) \cup(0, \infty) \)
\( \mathrm{S}_{4} \) : Number of points where \( f(x)=\frac{1}{\sin ^{-1}(\sin x)} \) is non-differentiable in the interval \( (0,3 \pi) \) is 3.
State, in order, whether \( \mathrm{S}_{1}, \mathrm{~S}_{2}, \mathrm{~S}_{3}, \mathrm{~S}_{4} \) are true or false
(A) TTTF
(B) TTTT
(C) FTTF
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