The Arrhenius equation expressing the effect of temperature on the rate constant of a reaction is

The rate constants $k_1$ and $k_2$ for two different reactions are $10^{16} \times e^{-2000/T}$ and $10^{15} \times e^{-1000/T}$ respectively. The temperature at which $k_1 = k_2$ is

The number of molecules with energy greater than the threshold energy for a reaction increases five-fold by a rise of temperature from $27^{\circ} C$ to $42^{\circ} C$. Its energy of activation in $J \ mol^{-1}$ is.............. (Take $\ln 5 = 1.6094$; $R = 8.314 \ J \ mol^{-1} K^{-1}$)

Half life of a first order reaction is $900 \ \text{min}$ at $400 \ K$. Find its half life at $300 \ K$. Given: $\frac{E_a}{2.303 \ R} = 1.3056 \times 10^3 \ K$. (in $\text{min}$)

The rate of a reaction quadruples when the temperature changes from $300 \, K$ to $310 \, K$. The activation energy of this reaction is ........... $kJ \, mol^{-1}$ (Assume activation energy and pre-exponential factor are independent of temperature; $\ln 2 = 0.693$; $R = 8.314 \, J \, mol^{-1} \, K^{-1}$)

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