A chemical reaction is carried out at two different temperatures $$T_1$$ and $$T_2$$ with $$T_2 > T_1$$, and also with and without a catalyst. The statement that is correct among the following is

Lowering in the activation energy of the reaction due to catalyst would be higher at $$T_2$$ than at $$T_1$$

Lowering in the activation energy of the reaction due to catalyst would be higher at $$T_1$$ than at $$T_2$$

The factor by which the rate of the reaction is increased by the catalyst would be lower at $$T_2$$ than at $$T_1$$

The factor by which the rate of the reaction is increased by the catalyst would be higher at $$T_2$$ than at $$T_1$$