What is the value of the slope of the plot $\ln K$ versus $\frac{1}{T}$ for a reaction having $E_{a} = 33.256 \ J \ mol^{-1}$?

For a reversible chemical reaction where the forward process is exothermic,which of the following statements is correct?

The activation energy for a reaction at the temperature $T \ K$ was found to be $2.303 \ RT \ J \ mol^{-1}$. The ratio of the rate constant to the Arrhenius factor is

Which of the following statements is correct?

For the following reactions:
$A \xrightarrow{700 \ K}$ Product
$A \xrightarrow[\text{catalyst}]{500 \ K}$ Product
it was found that $E_{a}$ is decreased by $30 \ kJ/mol$ in the presence of a catalyst. If the rate remains unchanged,the activation energy for the catalysed reaction is (Assume pre-exponential factor is same):

For the reaction $A \to B$,$K_1 = 10^8 \, e^{-6000/8.34T}$ and for the reaction $P \to Q$,$K_2 = 10^{10} \, e^{-8000/8.34T}$. At what temperature $T$ will $K_1 = K_2$ (in $K$)?