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

In respect of the equation $k = A e^{-E_a/RT}$ in chemical kinetics,which one of the following statements is correct?

Fill in the blanks:
$1.$ Common collision means ......... phenomenon in species.
$2.$ In collision theory,activation energy and proper orientation of the molecules together determine the ......... for an effective collision.

Calculate the activation energy of a reaction,whose rate constant doubles on raising the temperature from $300 \ K$ to $600 \ K$.

The activation energy of a first-order reaction at $25\,^{\circ}C$ is $30\,kJ/mol$. In the presence of a catalyst,the activation energy of the same reaction at $25\,^{\circ}C$ becomes $24\,kJ/mol$. The rate of the reaction in the presence of the catalyst will be how many times the original rate?

For a particular reaction,the rate constant becomes double on increasing temperature from $27^{\circ} C$ to $37^{\circ} C$. Calculate the approximate activation energy (in $kcal \ mol^{-1}$,$R=2 \ cal \ mol^{-1} \ K^{-1}$).