For a reaction,given below is the graph of $\ln k$ vs $\frac{1}{T}$. The activation energy for the reaction is equal to $...... \ cal \ mol^{-1}$. (Nearest integer). (Given : $R = 2 \ cal \ K^{-1} \ mol^{-1}$)

The decomposition of $A$ into product has a value of $k$ as $4.5 \times 10^{3} \, s^{-1}$ at $10^{\circ} C$ and an energy of activation of $60 \, kJ \, mol^{-1}$. At what temperature would $k$ be $1.5 \times 10^{4} \, s^{-1}$?

The correct reaction profile diagram for a positive catalyst reaction.

The time taken for half of the initial amount of $N_2O_5$ to decompose is $12 \ min$ at $310 \ K$ and $2 \ hrs$ at $300 \ K$. The activation energy of the reaction in $kJ \ mol^{-1}$ is $\left(R=8.3 \ J \ K^{-1} \ mol^{-1}\right)$

The rate of a certain biochemical reaction at physiological temperature $T$ occurs $10^{6}$ times faster with an enzyme than without. The change in the activation energy upon adding the enzyme is

For reactions $M, N, O$ and $P$,the activation energy order is $E_M < E_N < E_O < E_P$. For which reaction will the ratio $K_{310}/K_{300}$ be maximum?