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?

$A \rightarrow$ products ($1^{st}$ order reaction). Three sets of experiment were performed for a reaction under similar experimental conditions. Run $1 \Rightarrow 100 \ mL$ of $10 \ M$ solution of reactant $A$. Run $2 \Rightarrow 200 \ mL$ of $10 \ M$ solution of reactant $A$. Run $3 \Rightarrow 100 \ mL$ of $10 \ M$ solution of reactant $A + 100 \ mL$ of $H_2O$ added. The correct variation of rate of reaction is:

For the reaction $2 N_2O_{5(g)} \longrightarrow 4 NO_{2(g)} + O_{2(g)}$,the rate and rate constant are $1.02 \times 10^{-4} \ mol \ L^{-1} \ s^{-1}$ and $3.4 \times 10^{-5} \ s^{-1}$ respectively. What is the concentration of $N_2O_5$?

The rate of a reaction is given by $r = K[x][y] / [OH^-]$. If the concentration of $[OH^-]$ is increased,the order of the reaction will be ........

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?

In the reaction,$P + Q \longrightarrow R + S$,the time taken for $75 \%$ reaction of $P$ is twice the time taken for $50 \%$ reaction of $P$. The concentration of $Q$ varies with reaction time as shown in the figure. The overall order of the reaction is