What will be the effect on the fraction of molecules and the rate constant on increasing temperature?

The rate constant,$k$ for a first order reaction,$C_2H_5I_{(g)} \rightarrow C_2H_{4(g)} + HI_{(g)}$ is $x \ s^{-1}$ at $600 \ K$ and $4x \ s^{-1}$ at $700 \ K$. The energy of activation of the reaction (in $kJ \ mol^{-1}$) is (in $.16$)

Catalyst $A$ reduces the activation energy for a reaction by $10 \ kJ \ mol^{-1}$ at $300 \ K$. The ratio of rate $\frac{k_{T, \text{Catalysed}}}{k_{T, \text{Uncatalysed}}}$ is $e^{x}$. Find the value of $x$ [nearest integer].
[Assume that the pre-exponential factor is same in both the cases.
Given $R = 8.31 \ J \ K^{-1} \ mol^{-1}$]

The rate constant of a reaction increases by five times on increase in temperature from $27^{\circ} C$ to $52^{\circ} C$. The value of activation energy in $kJ \, mol^{-1}$ is $....$ . (Rounded-off to the nearest integer) $[R = 8.314 \, J \, K^{-1} \, mol^{-1}]$

For a first-order reaction,the time taken to complete $10\%$ at $298\, K$ is equal to the time taken to complete $25\%$ at $308\, K$. The activation energy of the reaction is ................ $kJ/mol$.

For a certain reaction,consider the plot of $\ln k$ versus $1/T$ given in the figure. If the rate constant of this reaction at $400 \ K$ is $10^{-5} \ s^{-1}$,then the rate constant at $500 \ K$ is: