Consider the following reaction

$$\mathrm{A}+\mathrm{B} \rightarrow \mathrm{C}$$

The time taken for A to become $$1 / 4^{\text {th }}$$ of its initial concentration is twice the time taken to become $$1 / 2$$ of the same. Also, when the change of concentration of B is plotted against time, the resulting graph gives a straight line with a negative slope and a positive intercept on the concentration axis.

The overall order of the reaction is ________.

Consider the two different first order reactions given below

$$\begin{aligned} & \mathrm{A}+\mathrm{B} \rightarrow \mathrm{C} \text { (Reaction 1) } \\ & \mathrm{P} \rightarrow \mathrm{Q} \text { (Reaction 2) } \end{aligned}$$

The ratio of the half life of Reaction 1 : Reaction 2 is $$5: 2$$ If $$t_1$$ and $$t_2$$ represent the time taken to complete $$2 / 3^{\text {rd }}$$ and $$4 / 5^{\text {th }}$$ of Reaction 1 and Reaction 2 , respectively, then the value of the ratio $$t_1: t_2$$ is _________ $$\times 10^{-1}$$ (nearest integer). [Given : $$\log _{10}(3)=0.477$$ and $$\log _{10}(5)=0.699$$]

Time required for $$99.9 \%$$ completion of a first order reaction is _________ times the time required for completion of $$90 \%$$ reaction.(nearest integer)

Consider the following single step reaction in gas phase at constant temperature.

$$2 \mathrm{~A}_{(\mathrm{g})}+\mathrm{B}_{(\mathrm{g})} \rightarrow \mathrm{C}_{(\mathrm{g})}$$

The initial rate of the reaction is recorded as $$\mathrm{r}_1$$ when the reaction starts with $$1.5 \mathrm{~atm}$$ pressure of $$\mathrm{A}$$ and $$0.7 \mathrm{~atm}$$ pressure of B. After some time, the rate $$r_2$$ is recorded when the pressure of C becomes $$0.5 \mathrm{~atm}$$. The ratio $$\mathrm{r}_1: \mathrm{r}_2$$ is _________ $$\times 10^{-1}$$. (Nearest integer)