For a reaction,$AB_5 \to AB + 4B$,the rate can be expressed in the following ways:
$-\frac{d[AB_5]}{dt} = K[AB_5]$ ; $\frac{d[B]}{dt} = K_1[AB_5]$
What is the correct relation between $K$ and $K_1$?

For the reaction $2 NO_{(g)} + 2 H_{2(g)} \longrightarrow N_{2(g)} + 2 H_2O_{(g)}$ with the rate law $\text{rate} = k[NO]^2[H_2]$,what is the order of reaction with respect to $H_2$ and the overall order of reaction,respectively?

The molecularity of the reaction of inversion of sugar is:

For a reaction $2NO_{(g)} + Cl_{2(g)} \rightleftharpoons 2NOCl_{(g)}$,when the concentration of $Cl_2$ is doubled,the rate of reaction becomes two times the original. When the concentration of $NO$ is doubled,the rate becomes four times. What is the order of the reaction?

The following data is given for the reaction between $A$ and $B$:

$S.NO.$	$[A] \ mol \ L^{-1}$	$[B] \ mol \ L^{-1}$	$Rate \ mol \ L^{-1} \ sec^{-1}$
$I$	$1 \times 10^{-2}$	$2 \times 10^{-2}$	$2 \times 10^{-4}$
$II$	$2 \times 10^{-2}$	$2 \times 10^{-2}$	$4 \times 10^{-4}$
$III$	$2 \times 10^{-2}$	$4 \times 10^{-2}$	$8 \times 10^{-4}$

Which of the following are correct statements?
$(a)$ Rate constant of the reaction is $1 \ mol^{-1} \ L \ sec^{-1}$.
$(b)$ Rate law of the reaction is $k[A][B]$.
$(c)$ Rate of reaction increases four times on doubling the concentration of both the reactants.

For a reaction $X + Y \to Z$,the rate is given by $\text{rate} \propto [X]$. What are $(i)$ the molecularity and $(ii)$ the order of the reaction?