For a reaction of order $(n - 1)$,what is the relationship between the half-life period $(t_{1/2})$ and the initial concentration of the reactant $([R]_0)$?

For a reaction $r = k[A][B]^2$,if the concentration of $A$ is doubled,the rate of reaction:

$A$ reaction is first order in terms of $A$ and second order in terms of $B$. What will be the rate of reaction,if the concentration of $B$ is increased two times?

Match List-$I$ with List-$II$:

List-$I$ (Order of Reaction)	List-$II$ (Unit of rate constant)
$A$. Zero order	$I$. $mol^{-1} L s^{-1}$
$B$. First order	$II$. $mol^{-2} L^{2} s^{-1}$
$C$. Second order	$III$. $s^{-1}$
$D$. Third order	$IV$. $mol L^{-1} s^{-1}$

For a reaction between $A$ and $B$,the order with respect to $A$ is $2$ and the order with respect to $B$ is $3$. If the concentrations of both $A$ and $B$ are doubled,the rate will increase by a factor of:

The rate constants for the following reactions are:
Reaction $1$: $A \xrightarrow{\text{catalyst } 1} P_1, k_1 = 1 \ s^{-1}$
Reaction $2$: $A \xrightarrow{\text{catalyst } 2} P_2, k_2 = 0.1 \ L \ mol^{-1} \ s^{-1}$
Reaction $3$: $A \xrightarrow{\text{catalyst } 3} P_3, k_3 = 0.01 \ L^2 \ mol^{-2} \ s^{-1}$
What is the correct relation between the rates of the reactions at $[A] = 1 \ M$?