For a reaction,$A + B \longrightarrow$ Product; the rate law is given by $r = k[A]^2[B]^{1/2}$. What is the order of the reaction?

For the reaction $A + B \rightarrow$ products,it is observed that
$(i)$ on doubling the initial concentration of $A$ only,the rate of reaction is also doubled and
$(ii)$ on doubling the initial concentration of both $A$ and $B$,there is a change by a factor of $8$ in the rate of the reaction.
The rate of this reaction is given by

The rate law for a reaction between reactants $A$,$B$,and $C$ is $r = K[A][B][C]^2$. If the concentration of $A$ is halved,then the rate of reaction:

Which among the following statements is $NOT$ true about rate constant?

Consider the plots for the types of reaction $nA \to B + C$. These plots respectively correspond to the reaction orders:

For the catalytic decomposition of $AB_3$, the half-life period is $4 \, \text{hours}$ at $50 \, \text{mm}$ and $2 \, \text{hours}$ at $100 \, \text{mm}$. What is the order of the reaction?