If $E_{cell}^{ɵ}$ for a given reaction is negative, which gives the correct relationships for the values of $\Delta G^{ɵ}$ and $K_{eq}$?a. $\Delta G^{\circ }>0,K_{eq}<1$ b. $\Delta G^{\circ }>0,K_{eq}>1$ c. $\Delta G^{\circ }<0,K_{eq}>1$ d. $\Delta G^{\circ }<0,K_{eq}<1$

A (a) Given, $E_{cell}^{\circ }=-ve$
The relation between $\Delta G^{\circ }\text{and}{E}_{cell}^{\circ }$ is given as
$\Delta G^{\circ }=-nF{E}_{cell}^{\circ }$…(i)
If $E_{cell}^{\circ }$ is negative, so $\Delta G^{\circ }$ comes out to be positive. Again, relation between $\Delta G^{\circ }$ and $K_{eq}$ is given as
$\Delta G^{\circ }=-2.303nRT{\log K}_{eq}$ ...(ii)
From Eq. (i) we get that $\Delta G^{\circ }$ is positive . Now , if $\Delta G^{\circ }$ is positive then $K_{eq}$ comes out to be negative from eq (ii).
i.e $\Delta G^{\circ }>1\text{and}{K}_{eq}<1$
Short trick As $E_{cell}^{\circ }$ is negative so reaction is non-spontaneous or you can say reaction is moving in backward direction. For non-spontaneous reaction. $\Delta G^{\circ }$ is always positive and $K_{eq}$ is always less than 1.