For a reaction $\frac{1}{2}\mathrm{A}\to 2\mathrm{B}$, the rate of disappearance of A is related to the rate of appearance ofB by the expression 

For the reaction $\frac{1}{2}\mathrm{A}\to 2\mathrm{B}$, rate of disappearance of A is related to rate of appearance of B by the expression:

$-\frac{1}{{\mathrm{V}}_{\mathrm{A}}}\frac{\mathrm{d}\left[\mathrm{A}\right]}{\mathrm{d}t}=\frac{1}{{\mathrm{V}}_{\mathrm{B}}}\frac{\mathrm{d}\left[\mathrm{B}\right]}{\mathrm{d}t}\text{ i.e. }-\frac{1}{(1/2)}\frac{\mathrm{d}\left[\mathrm{A}\right]}{\mathrm{d}t}=\frac{1}{2}\frac{\mathrm{d}\left[\mathrm{B}\right]}{\mathrm{d}t}\text{. }$Hence, $-\frac{\mathrm{d}\left[\mathrm{A}\right]}{\mathrm{d}t}=\frac{1}{4}\frac{\mathrm{d}\left[\mathrm{B}\right]}{\mathrm{d}t}$.

Hence, option C is correct.