1. Idea to use
   A molecule has net non-zero dipole moment if the bond dipoles do not cancel due to geometry/symmetry.

We must find the pair in which both compounds have non-zero dipole moments.

2. Check Option A: cis-butene, trans-butene

This refers to cis-2-butene and trans-2-butene.

• In cis-2-butene, the bond dipoles are on the same side, so they do not cancel completely. Hence, dipole moment is non-zero.
• In trans-2-butene, the structure is symmetric and the bond dipoles cancel. Hence, dipole moment is zero.

So, both are not non-zero.
Therefore, Option A is incorrect.

3. Check Option B: $\mathrm{CH_2Cl_2}$, $\mathrm{CHCl_3}$

Both are tetrahedral molecules.

• In $\mathrm{CH_2Cl_2}$, because two H and two Cl are attached to tetrahedral carbon, the bond dipoles do not cancel. So dipole moment is non-zero.
• In $\mathrm{CHCl_3}$, three C–Cl bond dipoles and one C–H bond dipole also do not cancel completely. So dipole moment is non-zero.

Thus, both compounds have non-zero dipole moments.
Therefore, Option B is correct.

4. Check Option C: Benzene, anisidine

• Benzene is highly symmetric, so its net dipole moment is zero.
• Anisidine (a substituted aromatic compound) generally has non-zero dipole moment.

Since benzene has zero dipole moment, both are not non-zero.
Therefore, Option C is incorrect.

5. Check Option D: 1,4-Dichlorobenzene, 1,3-Dichlorobenzene

• In 1,4-dichlorobenzene (para), the two identical C–Cl dipoles are opposite and cancel due to symmetry. So dipole moment is zero.
• In 1,3-dichlorobenzene (meta), the dipoles do not cancel completely. So dipole moment is non-zero.

Hence, both are not non-zero.
Therefore, Option D is incorrect.

6. Final conclusion

The only pair in which both compounds have net non-zero dipole moments is:

$\boxed{\text{B: } \mathrm{CH_2Cl_2},\ \mathrm{CHCl_3}}$