If \( f(x)=\left[\begin{array}{l}\frac{\sin \left[x^{2}\right] \pi}{x^{2}-3 x+8}+a x^{3}+b ; 0 \...
If \( f(x)=\left[\begin{array}{l}\frac{\sin \left[x^{2}\right] \pi}{x^{2}-3 x+8}+a x^{3}+b ; 0 \leq x \leq 1 \\ 2 \cos \pi x+\tan ^{-1} x ; 1x \leq 2\end{array} \quad\right. \) is differentiable in \( [0,2] \) then :
([.] denotes greatest integer function)
(a) \( a=\frac{1}{3} \)
(b) \( a=\frac{1}{6} \)
(c) \( b=\frac{\pi}{4}-\frac{13}{6} \)
(d) \( b=\frac{\pi}{4}-\frac{7}{3} \)
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