The specific rate constant of a $1^{st}$ order reaction depends on the

The rate of a reaction doubles,when the temperature is changed from $300 \ K$ to $310 \ K$. Activation energy of the reaction is....... $(R=8.314 \ J \ K^{-1} \ mol^{-1}, \log 2=0.301)$

Consider the given energy profile diagram for a reaction and choose the correct option:

For a reaction,the temperature increases from $10\,^\circ\text{C}$ to $50\,^\circ\text{C}$. The rate of the reaction will increase by a factor of ........

The rate of a reaction at $273 \ K$ is $R_0$. What will be the rate of the reaction at $313 \ K$? (Take the temperature coefficient as $2$)

The rate constant of a reaction depends on