Which is the unit of the rate constant for a second-order reaction?

For the reaction $A + B \to \text{Product}$,the rate of reaction becomes four times when the concentration of $A$ is doubled. If the rate of reaction does not change when the concentration of $B$ is doubled,the rate law for the reaction will be.....

For a reaction $2 \ A + B \rightarrow P$,when the concentration of $B$ alone is doubled,the rate does not change,and when the concentrations of both $A$ and $B$ are doubled,the rate increases by a factor of $4$. The unit of the rate constant is,

What is the order and molecularity respectively for the elementary reaction given below?
$O_{3(g)} + O_{(g)} \rightarrow 2O_{2(g)}$ if $r = k[O_3][O]$

The rate of the reaction: $2N_2O_5 \rightarrow 4NO_2 + O_2$ can be written in three ways.
$-\frac{d[N_2O_5]}{dt} = k[N_2O_5]$
$\frac{d[NO_2]}{dt} = k'[N_2O_5]$ ; $\frac{d[O_2]}{dt} = k''[N_2O_5]$
The relationship between $k$ and $k'$ and between $k$ and $k''$ are:

In a reaction,$A + B \rightarrow$ product,the rate is doubled when the concentration of $B$ is doubled,and the rate increases by a factor of $8$ when the concentrations of both the reactants $(A$ and $B)$ are doubled. The rate law for the reaction can be written as: