Here $(2\mathrm{\pi ct}/\mathrm{\lambda })$ as well as $(2\mathrm{\pi x}/\mathrm{\lambda })$ arc dimensionless. So unit of ct is same as that of $\mathrm{\lambda }$. Unit of x is same as that of $\mathrm{\lambda }$. Also,

$\left[\frac{2\mathrm{\pi ct}}{\mathrm{\lambda }}\right]=\left[\frac{2\mathrm{\pi x}}{\mathrm{\lambda }}\right]={\mathrm{M}}^0{\mathrm{L}}^0{\mathrm{T}}^0$

Hence, $\left[\frac{2\mathrm{\pi c}}{\mathrm{\lambda }}\right]=\left[\frac{2\mathrm{\pi x}}{\mathrm{\lambda t}}\right]$,, option (d),$\mathrm{x}/\mathrm{\lambda }$ is unitless. This is not the case with $\mathrm{c}/\mathrm{\lambda }$.