Activation energy of any reaction depends on

The rate constant of a first order reaction was doubled when the temperature was increased from $300 \ K$ to $310 \ K$. What is its approximate activation energy (in $kJ \cdot mol^{-1}$)? ($R = 8.3 \ J \cdot mol^{-1} \cdot K^{-1}$; $\log 2 = 0.3$)

Which one of the following is true for an exothermic reaction $A \rightleftharpoons B$, if $E_f$ and $E_b$ are the activation energies of forward and backward reactions respectively?

$A$ sample of milk splits after $60 \; min.$ at $300 \; K$ and after $40 \; min.$ at $400 \; K$ when the population of $Lactobacillus \; acidophilus$ in it doubles. The activation energy (in $kJ / mol$) for this process is closest to ............. $kJ / mol$.
(Given: $R = 8.3 \; J \; mol^{-1} \; K^{-1}$,$\ln(1.5) = 0.405$)

The number of given statement/s which is/are correct is $.....$.
$(A)$ The stronger the temperature dependence of the rate constant,the higher is the activation energy.
$(B)$ If a reaction has zero activation energy,its rate is independent of temperature.
$(C)$ The stronger the temperature dependence of the rate constant,the smaller is the activation energy.
$(D)$ If there is no correlation between the temperature and the rate constant then it means that the reaction has negative activation energy.

For a first order reaction,a plot of $\ln k$ ($y$-axis) and $\frac{1}{T}$ ($x$-axis) gave a straight line with a slope equal to $-10^3 \ K$ and an intercept equal to $2.303$ (on $y$-axis). What is the activation energy ($E_a$ in $kJ \ mol^{-1}$) of the reaction? (Given $R = 8.314 \ J \ mol^{-1} \ K^{-1}$)