The correct statements among the following are. A. Basic vanadium...

Statement A: Vanadium pentoxide ($\text{V}_2\text{O}_5$) is used as a catalyst in the manufacture of $\text{H}_2\text{SO}_4$ by the Contact process. $\text{V}_2\text{O}_5$ is an amphoteric oxide, not a basic oxide. Thus, statement A is incorrect.

Statement B: The transition metal halide used in Ziegler-Natta polymerization is $\text{TiCl}_4$. In $\text{TiCl}_4$, titanium is in the $+4$ oxidation state with a $3\text{d}^0$ electronic configuration. The number of unpaired electrons is zero, so its spin-only magnetic moment is $0$ BM. Thus, statement B is incorrect.

Statement C: The p-block metal compound used in Ziegler-Natta polymerization is triethylaluminium, $\text{Al}(\text{C}_2\text{H}_5)_3$. Aluminium is a p-block element and is in the $+3$ oxidation state. Thus, statement C is correct.

Statement D: The metal halide employed in the Wacker process is $\text{PdCl}_2$. Palladium (Pd) has the electronic configuration $[\text{Kr}] 4\text{d}^{10}$. In $\text{PdCl}_2$, Pd is in the $+2$ oxidation state, giving it a $4\text{d}^8$ configuration. The number of electrons in the outermost d-orbital is $8$. Thus, statement D is correct.

Therefore, only statements C and D are correct.