A flask is filled with equal moles of $\mathrm{A}$ and $\mathrm{B}$. The half lives of $\mathrm{A}$ and $\mathrm{B}$ are $100 \mathrm{s}$ and $50 \mathrm{s}$ respectively and are independent of the initial concentration. The time required for the concentration of $\mathrm{A}$ to be four times that of $\mathrm{B}$ is____$\mathrm{s}$.
(Given : $\ln 2=0.693$)

The rate constant for a first order reaction is given by the following equation :

$\mathrm{lnk}=33.24-\frac{2.0\times {10}^4 \mathrm{K}}{ \mathrm{T}}$

The Activation energy for the reaction is given by ${\mathrm{kJmol}}^{-1}$. (In Nearest integer) (Given : $\mathrm{R}=8.3 \mathrm{J}{ \mathrm{K}}^{-1}{ \mathrm{mol}}^{-1}$)

The equation $\mathrm{k}=\left(6.5\times {10}^{12}{ \mathrm{s}}^{-1}\right){\mathrm{e}}^{-26000 \mathrm{K}/\mathrm{T}}$ is followed for the decomposition of compound $\mathrm{A}$. The activation energy for the reaction is ____ $\mathrm{KJ} {\mathrm{mol}}^{-1}$. [nearest integer]

(Given: $\mathrm{R}=8.314 \mathrm{J}{ \mathrm{K}}^{-1}{ \mathrm{mol}}^{-1}$)

For the decomposition of azomethane. ${\mathrm{CH}}_3{ \mathrm{N}}_2{\mathrm{CH}}_3\left(\mathrm{g}\right)\to {\mathrm{CH}}_3{\mathrm{CH}}_3\left(\mathrm{g}\right)+{\mathrm{N}}_2$ a first order reaction, the variation in partial pressure with time at $600 \mathrm{K}$ is given as

The half life of the reaction is____$\times {10}^{-5} \mathrm{s}$