The correct thermodynamic conditions for the spontaneous reaction at all temperatures is

The correct thermodynamic conditions for the spontaneous reaction at all temperatures is

$∆\mathrm{H}<0$ and $∆\mathrm{S}>0$

Under these conditions, $\Delta \mathrm{G}=\Delta \mathrm{H}-\mathrm{T}\Delta \mathrm{S}<0$

The correct thermodynamic conditions for the spontaneous reaction at all temperatures is $∆\mathrm{H}<0$ and $∆\mathrm{S}>0$

Under these conditions, $\Delta \mathrm{G}=\Delta \mathrm{H}-\mathrm{T}\Delta \mathrm{S}<0$

Note: for spontaneous reactions, $\Delta \mathrm{G}<0$, for non spontaneous reactions, $\Delta \mathrm{G}>0$, for reactions at equilibrium, $\Delta \mathrm{G}=0$

Hence the correct answer is (C) $\Delta \mathrm{H}<0$ and $\Delta \mathrm{S}>0$.