Select correct statement(s) about role of catalyst for a reaction

(1) ${\mathrm{\Delta G}}^{\circ }=-2.303 \mathrm{RT} \log {\mathrm{K}}_{\mathrm{c}}$

Since, K_c remains unchanged in the presence of a catalyst, thus $∆\mathrm{G}°$ is not affected correct.

(2) In the presence of catalyst, reaction path of lower activation energy is taken Correct

(3) In the presence of catalyst, reaction path of lower activation energy is taken Correct.

(4) Nor spontaneous reactions are not catalysed. correct.