1. Examine Assertion (A)

Assertion:

• There is a considerable increase in covalent radius from $\mathrm{N}$ to $\mathrm{P}$.
• From $\mathrm{As}$ to $\mathrm{Bi}$ only a small increase in covalent radius is observed.

For group 15 elements, the covalent radius generally increases down the group, but not uniformly.

Approximate trend: $\mathrm{N} < \mathrm{P} < \mathrm{As} \approx \mathrm{Sb} \approx \mathrm{Bi}$

• The increase from $\mathrm{N}$ to $\mathrm{P}$ is indeed large because we move from the 2nd period to the 3rd period.
• From $\mathrm{As}$ to $\mathrm{Sb}$ to $\mathrm{Bi}$, the increase is relatively small due to poor shielding by intervening $d$ and $f$ electrons, causing contraction effects.

So, Assertion (A) is true.

2. Examine Reason (R)

Reason:

• Covalent and ionic radii in a particular oxidation state increase down the group.

This is a generally correct periodic trend:

• On moving down a group, additional shells are added.
• Hence atomic size, covalent radius, and ionic radius generally increase.

So, Reason (R) is true.

3. Check whether (R) correctly explains (A)

The reason only states the general trend that radii increase down the group.

But Assertion (A) is about a non-uniform increase:

• large increase from $\mathrm{N}$ to $\mathrm{P}$,
• only small increase from $\mathrm{As}$ to $\mathrm{Bi}$.

This non-uniformity is explained by poor shielding of $d$ and $f$ electrons and resulting contraction effects, not merely by the general statement that radii increase down the group.

Therefore, (R) is not the correct explanation of (A).

4. Evaluate options

• A: (A) is false but (R) is true $\rightarrow$ False
• B: Both (A) and (R) are true and (R) is the correct explanation of (A) $\rightarrow$ False
• C: Both (A) and (R) are true but (R) is not the correct explanation of (A) $\rightarrow$ True
• D: (A) is true but (R) is false $\rightarrow$ False

5. Final Answer

The correct option is: $\boxed{\text{C}}$

6. Comparison with stored correct answer

Stored correct answer: C

My derived answer: C

So, they agree.