The pair having identical value of $\large\frac{e}{m}$:

$\begin{array}{1 1}(a)\;\text{A proton and a neutron}\\(b)\;\text{A proton and a deuterium ion}\\(c)\;\text{An }\alpha-\text{Particle and a deuterium ion}\\(d)\;\text{An electron and } \gamma \text{-rays}\end{array}$

$\large\frac{e}{m}$ ratio for $\alpha$-particle=$\Large\frac{2}{4} = \Large\frac{1}{2}$
For deuterium ion =$\large\frac{1}{2}$
Hence (c) is the correct answer.
edited Mar 19, 2014