Key property of a diamagnetic material

For a diamagnetic material, the magnetic susceptibility is negative: $\chi_m < 0$ Since $\mu_r = 1 + \chi_m,$ therefore for a diamagnetic material, $\mu_r < 1$ (and generally slightly less than 1, but the key condition is just $\mu_r<1$).

Condition on relative permittivity

For ordinary materials, relative permittivity must be positive: $\varepsilon_r > 0$ So both $0.5$ and $1.5$ are allowed in principle.

Check each option

• Option A: $\varepsilon_r=0.5,\ \mu_r=1.5$

  Here, $\mu_r=1.5>1$ This corresponds to a paramagnetic-type behavior, not diamagnetic.

  So, A is not allowed.

• Option B: $\varepsilon_r=1.5,\ \mu_r=0.5$

  Here, $\mu_r=0.5<1$ This satisfies the diamagnetic condition. Also $\varepsilon_r=1.5>0$ is allowed.

  So, B is allowed.

• Option C: $\varepsilon_r=0.5,\ \mu_r=0.5$

  Here, $\mu_r=0.5<1$ so magnetically it is diamagnetic, and $\varepsilon_r=0.5>0$ is also allowed.

  So, C is also allowed.

• Option D: $\varepsilon_r=1.5,\ \mu_r=1.5$

  Here, $\mu_r=1.5>1$ so it is not diamagnetic.

  Thus, D is not allowed.

Conclusion

The values allowed for a diamagnetic material are: $\boxed{\text{B and C}}$

Comparison with stored answer

The stored correct answer is B, but from the physics condition for diamagnetism, both B and C satisfy $\mu_r<1$ and have positive $\varepsilon_r$.

Hence, I do not agree with the stored answer.