If doubling the concentration of a reactant $A$ increases the rate $4$ times and tripling the concentration of $A$ increases the rate $9$ times,the rate is proportional to

For the reaction $2A + B \rightarrow C$,the rate law is given by $\text{Rate} = k[A][B]$. Which of the following statements is correct for this reaction?

The half-life periods of decomposition of $PH_3$ for different initial pressures are given below $:$

Initial Pressure $p$ (torr)	$707$	$79$	$37.5$
Half-life $t_{1/2}$ (min)	$84$	$84$	$84$

Determine the order of the reaction.

The reaction $2A + B_{2} \rightarrow 2AB$ is an elementary reaction. For a certain quantity of reactants,if the volume of the reaction vessel is reduced by a factor of $3,$ the rate of the reaction increases by a factor of $.....$. (Round off to the Nearest Integer).

$A$ 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?

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