1. Permanent dipole moment depends on molecular geometry

A molecule has a permanent dipole moment if:

• it contains polar bonds, and
• the vector sum of bond dipoles does not cancel.

So we must check the shape of each molecule.

2. Analyze each molecule

(i) $CO_2$

• Structure: linear
• Bond dipoles: two $C=O$ bond dipoles are equal and opposite

Therefore, $\mu_{CO_2}=0$ So $CO_2$ has no permanent dipole moment.

(ii) $SiF_4$

• Structure: tetrahedral and symmetric
• All four $Si-F$ bonds are polar, but arranged symmetrically

Hence all bond dipoles cancel: $\mu_{SiF_4}=0$ So $SiF_4$ has no permanent dipole moment.

(iii) $NO_2$

• Structure: bent (angular)
• Because of the bent geometry, bond dipoles do not cancel

Thus, $\mu_{NO_2} \neq 0$ So $NO_2$ has a permanent dipole moment.

(iv) $O_3$

• Structure: bent
• Due to bent geometry, the bond dipoles do not cancel

Therefore, $\mu_{O_3} \neq 0$ So $O_3$ also has a permanent dipole moment.

3. Check each option

A: $NO_2$ and $CO_2$

• $NO_2$: polar
• $CO_2$: non-polar

So this is incorrect.

B: $NO_2$ and $O_3$

• $NO_2$: polar
• $O_3$: polar

So this is correct.

C: $SiF_4$ and $CO_2$

• $SiF_4$: non-polar
• $CO_2$: non-polar

So this is incorrect.

D: $SiF_4$ and $NO_2$

• $SiF_4$: non-polar
• $NO_2$: polar

So this is incorrect.

4. Final Answer

The pair in which both molecules have permanent dipole moments is: $\boxed{B\; (NO_2\text{ and }O_3)}$