(A) $\mathrm{M}\left(\mathrm{s}\right)+2{\mathrm{H}}^{+}\left(\mathrm{aq}\right)\to {\mathrm{H}}_2\left(\mathrm{g}\right)+{\mathrm{M}}^{2+}\left(\mathrm{aq}\right)$

if $\frac{{\mathrm{dE}}_{\mathrm{cell} }}{\mathrm{dT}}=\frac{\mathrm{R}}{\mathrm{F}}$

$\Delta \mathrm{S}=\mathrm{nF}\frac{\mathrm{dE}}{\mathrm{dT}}=2 \mathrm{F}\left(\frac{\mathrm{R}}{\mathrm{F}}\right)=2R$

(B) ${\mathrm{E}}_{\mathrm{cell} }=\frac{-2.303\mathrm{RT}}{\mathrm{F}}\log \frac{0.01}{0.1}=\frac{2.303\mathrm{RT}}{\mathrm{F}}$

$\frac{{\mathrm{dE}}_{\mathrm{cell} }}{\mathrm{dT}}=\frac{2.303\mathrm{R}}{\mathrm{F}}$

$\therefore \Delta \mathrm{S}=\mathrm{nF}\frac{\mathrm{dE}}{\mathrm{dT}}>0$

It is an entropy driven process.

(C) It is correct

Racemisation is a thermodynamically favourable method, and it proceeds spontaneously if a suitable pathway is accessible for the interconversion of the enantiomers. 

During racemisation of optically active compound, disorderness increases and hence, entropy increases.

(D) For ${\left[\mathrm{Ni}{\left({\mathrm{H}}_2\mathrm{O}\right)}_6\right]}^{2+}+3\mathrm{en}\to {\left[\mathrm{Ni}{\left(\mathrm{en}\right)}_3\right]}^{+3}+6{\mathrm{H}}_2\mathrm{O}$
Entropy increases when bidentate ligands replace monodentate ligands due to increase in the number of molecules on the product side.

Hence, (B, C, D) are correct.