For the reaction,$XA + YB \rightarrow ZC$,if $\frac{- d [ A ]}{ dt } = \frac{- d [ B ]}{ dt } = \frac{d [ C ]}{ dt },$ then the correct statement among the following is:

If the rate of disappearance of $N_2O_5$ in the following reaction is $1.2 \times 10^{-5} \ mol \ L^{-1} \ s^{-1}$,the rate of production of $NO_2$ in $mol \ L^{-1} \ s^{-1}$ is:
$2N_2O_{5(g)} \longrightarrow 4NO_{2(g)} + O_{2(g)}$

For the reaction $2A + 3B \rightarrow 4C$,the rate of reaction is expressed as:

At $298 \ K$ the value of $-\frac{\Delta[Br^{-}]}{\Delta t}$ for the reaction$5Br^-{_{\text{(aq)}}} + BrO_3^-{_{\text{(aq)}}} + 6H^+{_{\text{(aq)}}} \rightarrow 3Br_{2\text{(aq)}} + 3H_2O_{\text{(l)}}$ is $x \ mol \ L^{-1} \ min^{-1}$. What is the rate (in $mol \ L^{-1} \ min^{-1}$) of this reaction?

$A \rightarrow P$ is a first-order reaction. The following graph is obtained for this reaction ($x$-axis $=$ time,$y$-axis $=$ concentration of $A$). The instantaneous rate of the reaction at point $C$ is:

Fill in the blanks:
$(a)$ Catalyst ......... the rate of reaction.
$(b)$ Inhibitor ......... the rate of the reaction.
$(c)$ If temperature increases,the rate of reaction ......... .