One of the synthetic auxin is

Opening of flowers in the cymose inflorescence is

Consider the reaction:
$Cl_{2(aq)} + H_2S_{(aq)} \to S_{(s)} + 2H^{+}_{(aq)} + 2Cl^{-}_{(aq)}$
The rate equation for this reaction is $\text{rate} = k[Cl_2][H_2S]$. Which of these mechanisms is/are consistent with this rate equation?
$A.$ $Cl_2 + H_2S \to H^{+} + Cl^{-} + Cl^{+} + HS^{-}$ (slow)
$Cl^{+} + HS^{-} \to H^{+} + Cl^{-} + S$ (fast)
$B.$ $H_2S \rightleftharpoons H^{+} + HS^{-}$ (fast equilibrium)
$Cl_2 + HS^{-} \to 2Cl^{-} + H^{+} + S$ (slow)

Smooth muscles are:

Let $f(x)=e^x$,$g(x)=\sin ^{-1} x$ and $h(x)=f(g(x))$,then $\frac{h^{\prime}(x)}{h(x)}$ is equal to

$\int_0^\pi \frac{\theta \sin \theta}{1+\cos ^2 \theta} d \theta$ is equal to