When a sample of an unknown material is placed in a non-uniform...

When a material is placed in a non-uniform magnetic field and experiences a net force driving it from the stronger to the weaker part of the field, it exhibits diamagnetism.

For diamagnetic materials, the magnetic susceptibility $\chi$ is small and negative, i.e., $-1 < \chi < 0$.

The relative permeability $\mu_r$ is related to magnetic susceptibility by the relation $\mu_r = 1 + \chi$.

Since $\chi$ is small and negative, $\mu_r$ must be slightly less than $1$.

Checking the given options, only $\chi = -0.004$ and $\mu_r = 0.996$ satisfy both conditions ($\chi < 0$ and $\mu_r = 1 - 0.004 = 0.996$).

Answer: $\chi = -0.004$, $\mu_r = 0.996$