Recall molecular shapes and dipole moment idea

Dipole moment depends on:

• bond polarity, and
• molecular geometry (whether bond dipoles cancel or not).

If the vector sum of all bond dipoles is zero, the molecule has zero dipole moment.

Check each option

A. $\mathrm{CH}_4$

• Shape: tetrahedral
• All four $\mathrm{C-H}$ bonds are symmetrically arranged.
• Their dipole moments cancel completely.

Hence, $\mu(\mathrm{CH}_4)=0$

B. $\mathrm{NF}_3$

• Shape: trigonal pyramidal
• $\mathrm{N-F}$ bonds are polar.
• However, in $\mathrm{NF}_3$, the bond dipoles and the lone pair effect oppose each other, so the net dipole moment is small.

Thus, $\mathrm{NF}_3$ has a small but nonzero dipole moment.

C. $\mathrm{NH}_3$

• Shape: trigonal pyramidal
• $\mathrm{N-H}$ bond dipoles are directed such that they reinforce the direction associated with the lone pair.
• Therefore, the net dipole moment is appreciable.

In fact, $\mu(\mathrm{NH}_3) > \mu(\mathrm{NF}_3)$

D. $\mathrm{PF}_5$

• Shape: trigonal bipyramidal
• Symmetrical arrangement causes cancellation of bond dipoles.

Hence, $\mu(\mathrm{PF}_5)=0$

Comparison

• $\mathrm{CH}_4$: $0$
• $\mathrm{PF}_5$: $0$
• $\mathrm{NF}_3$: small
• $\mathrm{NH}_3$: largest among these

Final answer

The molecule with maximum dipole moment is: $\boxed{\mathrm{NH}_3}$

So, the correct option is C.