The half-life of a first order reaction varies with temperature according to

The temperature coefficient of a reaction is defined as:

$A$ rise in temperature increases the velocity of a reaction. It is because it results in

The first order rate constant $k$ is related to temperature $T$ as $\log \, k = 15.0 - (10^{6} / T)$. Which of the following pairs of values for the Arrhenius factor $A$ and activation energy $E_a$ is correct?

The rate of a chemical reaction doubles for every $10\,^{\circ}C$ rise in temperature. If the temperature is increased to $50\,^{\circ}C$ from $0\,^{\circ}C$,by how many times will the rate of reaction increase?

Consider the following statements related to the temperature dependence of rate constants. Identify the correct statements:
$A.$ The Arrhenius equation holds true only for an elementary homogeneous reaction.
$B.$ The unit of $A$ is the same as that of $k$ in the Arrhenius equation.
$C.$ At a given temperature,a low activation energy means a fast reaction.
$D.$ $A$ and $E_a$ as used in the Arrhenius equation depend on temperature.
$E.$ When $E_a > RT$,$A$ and $E_a$ become interdependent.
Choose the correct answer from the options given below: