Which statement is true with respect to a catalyst?

The enthalpy $(H)$ of an elementary exothermic reaction,$A \rightleftharpoons B$ is schematically plotted against the reaction coordinate. The plots in the presence and absence of a catalyst are shown in dashed and solid lines,respectively. Identify the correct plot for the reaction.

The velocity of the chemical reaction doubles every $10^\circ C$ rise of temperature. If the temperature is raised by $50^\circ C$,the velocity of the reaction increases to about .......... times.

The rate constant $(K')$ of one reaction is double the rate constant $(K'')$ of another reaction. What is the relationship between the corresponding activation energies of the two reactions (${E_a}'$ and ${E_a}''$)?

For a first order reaction,the rate of reaction is $2.4 \times 10^{-3} \ mol \ L^{-1} \ s^{-1}$ at $27 \ ^\circ C$. The activation energy of the reaction is $24.942 \ kJ \ mol^{-1}$. The rate of reaction at $327 \ ^\circ C$ is ....... $mol \ L^{-1} \ s^{-1}$ [Take $e^5 = 150$,$e^{0.005} = 1$,$e^4 = 55$].

The minimum energy required for molecules to participate in a chemical reaction is called $.......$.