(a) It is the magnitude difference in energy between the two sets of d-orbital i,e $t_{2g}$ and eg. electronic configuration of $d^5$ if $\Delta_0 > P$ is $t_{2g}^5$ eg Because in a strong field ligand pairing of electrons takes place for eg $[\mathrm{Ni}(\mathrm{CN})_4]^{2-}$ $-\mathrm{CN}$ is a strong field ligand(b) $\mathrm{Ni}=28,3 d^8 4 s^2$ $\mathrm{Ni}^{2+}=3 d^8 4 s^0$ $[\mathrm{Ni}(\mathrm{CN})_4]$ is a strong field ligand.$=dsp^2$ hybridization showing square planar geometry $=$ All electrons are paired so it is diamagnetic in nature. $[\mathrm{Ni}(\mathrm{CO})_4]$ $\mathrm{Ni}=28,3 d^8 4 s^2$ $\mathrm{Ni}=$ valency is zero $=sp^3$ hybridization $\rightarrow$ showing tetrahedral geometry $\rightarrow$ All electrons are paired so it is diamagnetic in nature.