1. Geometry of both molecules

Both $\mathrm{NH_3}$ and $\mathrm{NF_3}$ are trigonal pyramidal due to one lone pair on nitrogen.

So, the net dipole moment depends on:

• dipole due to the three bond moments
• dipole due to the lone pair (orbital dipole)

2. Statement I analysis

Statement I says:

Since fluorine is more electronegative than nitrogen, the net dipole moment of $\mathrm{NF_3}$ is greater than $\mathrm{NH_3}$.

This is false.

Reason:

• In $\mathrm{NH_3}$, each $\mathrm{N-H}$ bond dipole is directed towards nitrogen because $\mathrm{N}$ is more electronegative than $\mathrm{H}$.
• The lone pair on nitrogen also creates an orbital dipole in the same general direction as the resultant of bond dipoles.
• Therefore, in $\mathrm{NH_3}$, these effects add up, giving a relatively larger dipole moment.

For $\mathrm{NF_3}$:

• Each $\mathrm{N-F}$ bond dipole is directed towards fluorine.
• The resultant of the bond dipoles is opposite to the lone pair dipole.
• Hence, they partially cancel, making the net dipole moment small.

Indeed,

So Statement I is false.

3. Statement II analysis

Statement II says:

In $\mathrm{NH_3}$, the orbital dipole due to lone pair and the dipole moment of $\mathrm{NH}$ bonds are in opposite direction, but in $\mathrm{NF_3}$ the orbital dipole due to lone pair and dipole moments of $\mathrm{N-F}$ bonds are in same direction.

This is also false because the actual situation is the reverse.

For $\mathrm{NH_3}$:

• Bond dipoles of $\mathrm{N-H}$ point toward nitrogen.
• The lone pair dipole is also on nitrogen side.
• Thus, they are in the same direction, not opposite.

For $\mathrm{NF_3}$:

• Bond dipoles of $\mathrm{N-F}$ point toward fluorine atoms.
• The lone pair dipole is on nitrogen side.
• Thus, they are in opposite directions, not same.

So Statement II is false.

4. Conclusion

• Statement I: False
• Statement II: False

Therefore, the correct option is:

5. Comparison with stored answer

Stored correct answer = $\boxed{\text{C}}$

My derived answer also = $\boxed{\text{C}}$

So, the answer agrees with the stored correct answer.