Chemical Kinetics question bank (Chemistry)

Given below are two statements:
$R=8.314$ J K$^{-1}$ mol$^{-1}$ and $1$ cal $=4.2$ J
Statement I: When $E_a=12.6$ kcal/mol, the room temperature rate constant is doubled by a $10\,^\circ$C increase in temperature ($298$ K to $308$ K)
Statement II: For a first order reactions A $\rightarrow$ B,

Here $[A]_o$ is the initial concentration of A and $t_{1/2}$ is half life of reaction.
In the light of the above statements, choose the correct answer from the options given below:

Decomposition of a hydrocarbon follows the equation $k = (5.5 \times 10^{11}\,\text{s}^{-1})\,e^{\frac{-28000\,\text{K}}{T}}$. The activation energy of reaction is __________ kJ mol$^{-1}$. (Nearest Integer) Given : R $= 8.3$ J K$^{-1}$ mol$^{-1}$