Question
$\mathop {\lim }\limits_{\theta \to \frac{\pi }{2}} \frac{{\frac{\pi }{2} - \theta }}{{\cot \theta }} =$
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$f(x)= \begin{cases}\operatorname{a} \sin \frac{\pi}{2}(x-1), & \text { for } x \leq 0 \\ \frac{\tan 2 x-\sin 2 x}{b x^{3}}, & \text { for } x>0\end{cases}$
If $f$ is continuous at $x=0$, then $10-a b$ is equal to ...... .
$\left| {1 - {{\log }_{\frac{1}{6}}}x} \right| + \left| {{{\log }_2}x} \right| + 2 = \left| {3 - {{\log }_{\frac{1}{6}}}x + {{\log }_{\frac{1}{2}}}x} \right|$ is $\left[ {\frac{a}{b},a} \right],a,b, \in N,$ then the value of $(a + b)$ is