Step: Analyse all the options.
$\text{Given: $|A|=2$ and $|B|=4$}\\ (a) ~\vec A.\vec B=A B \cos \theta=0 \\ \Rightarrow \quad 2 \times 4 \cos \theta=0 \\ \Rightarrow \quad \cos \theta=0=\cos 90^{\circ} \\ \Rightarrow \quad \theta=90^{\circ} \\\text{Therefore, option (a) matches with option (ii)}.$

$(b) ~\vec A. \vec B=AB \cos \theta=8 \\ \\ \Rightarrow \quad 2 \times 4 \cos \theta=8 \\\Rightarrow \quad \cos \theta=1=\cos0^{\circ}\Rightarrow \theta= 0^{\circ} \\\text{Therefore, option (b) matches with option (i)}.$

$(c) ~ \vec A.\vec B= A B \cos \theta=4 \\\Rightarrow 2 \times 4 \cos \theta=4 \\ \Rightarrow \cos \theta=\frac{1}{2}=\cos 60^{\circ} \Rightarrow \theta=60^{\circ} \\ \text{Therefore, option (c) matches with option (iv)}.$

$(d) ~ \vec A.\vec B=AB \cos \theta=-8 \\ \Rightarrow 2 \times 4 \cos \theta=-8 \\ \Rightarrow \cos \theta=-1=\cos 180^{\circ} \\\Rightarrow \theta=180^{\circ} \\ \text{Therefore, option (d) matches with option (iii).}$
Therefore, the correct match is $\mathrm{(a)}\rightarrow(\mathrm{ii}); \mathrm{(b)}\rightarrow(\mathrm{i});\mathrm{(c)}\rightarrow(\mathrm{iv});\mathrm{(d)}\rightarrow(\mathrm{iii})$
Hence, option (2) is the correct answer.