For the reaction, $\mathrm{aA}+\mathrm{bB}\to \mathrm{cC}+\mathrm{dD},$ the plot of $\log \mathrm{k}$ v/s $\frac{1}{ \mathrm{T}}$ is given below:

The temperature at which the rate constant of the reaction is ${10}^{-4} {\mathrm{s}}^{-1}$ is _____ $\mathrm{K}.$
(Rounded-off to the nearest integer) [Given : The rate constant of the reaction is ${10}^{-5} {\mathrm{s}}^{-1}$ at $500 \mathrm{K}$.]

Sucrose hydrolyses in acid solution into glucose and fructose following first order rate law with a half-life of $3.33 \mathrm{h}$ at $25°\mathrm{C}.$ After $9 \mathrm{h},$ the fraction of sucrose remaining is $\mathrm{f}.$ The value of ${\log }_{10}\left(\frac{1}{\mathrm{f}}\right)$ is ________ $\times {10}^{-2}.$ (Rounded off to the nearest integer)

[Assume: In$10=2.303, \ln 2=0.693$]

${\mathrm{PCl}}_5\left(\mathrm{g}\right)\to {\mathrm{PCl}}_3\left(\mathrm{g}\right)+{\mathrm{Cl}}_2\left(\mathrm{g}\right)$

In the above first order reaction the concentration of ${\mathrm{PCl}}_5$ reduces from initial concentration $50 \mathrm{mol}{ \mathrm{L}}^{-1}$ to $10 \mathrm{mol}{ \mathrm{L}}^{-1}$ in $120$ minutes at $300 \mathrm{K}.$ The rate constant for the reaction at $300 \mathrm{K}$ is $\mathrm{x}\times {10}^{-2}{ \min }^{-1}.$ The value of $\mathrm{x}$ is __________.

[Given $\log 5=0.6989$]

The results given in the below table were obtained during kinetic studies of the following reaction: $2\mathrm{A}+\mathrm{B}\to \mathrm{C}+\mathrm{D}$

X and Y in the given table are respectively :