What is the slope of the straight line for the graph drawn between $\ln k$ and $\frac{1}{T}$,where $k$ is the rate constant of a reaction at temperature $T$?

Plots showing the variation of the rate constant $k$ with temperature $T$ are given below. The plot that follows Arrhenius equation is

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

What is the slope of the graph between $\ln K$ and $\frac{1}{T}$ according to the Arrhenius equation?

The rate constant,the activation energy and the Arrhenius parameter of a chemical reaction at $25\,^oC$ are $3.0 \times 10^{-4}\,s^{-1}$,$104.4\,kJ\,mol^{-1}$ and $6.0 \times 10^{14}\,s^{-1}$ respectively. The value of the rate constant as $T \to \infty$ is

When temperature is increased from $27\,{}^{\circ}C$ to $127\,{}^{\circ}C$,the rate of reaction becomes doubled. The activation energy $E_a$ will be ........ $kCal$.