1. Meaning of $pK_b$

For bases, $pK_b = -\log K_b$ A smaller $pK_b$ means a stronger base, and a larger $pK_b$ means a weaker base.

So we must arrange the given compounds in increasing order of $pK_b$, i.e. from strongest base to weakest base.

2. Basicity trend of amines/aniline-type compounds

The basicity depends on the availability of the lone pair on nitrogen.

• If the lone pair is more available, the compound is more basic.
• If the lone pair is delocalized by resonance or withdrawn by a $-I$ effect, the compound is less basic.

For aromatic amines:

• Electron-donating groups increase basicity.
• Electron-withdrawing groups decrease basicity.

For aliphatic amines:

• Alkyl groups generally increase electron density on nitrogen by $+I$ effect, making them more basic than aniline-type bases.

3. Relative order among the given compounds

From the structures labeled $(A),(B),(C),(D)$, the compound $(B)$ has the most available lone pair on nitrogen, so it is the strongest base.

Next is $(D)$, which is less basic than $(B)$ but more basic than the aromatic/resonance-stabilized cases.

Between $(A)$ and $(C)$, $(A)$ is more basic than $(C)$ because in $(C)$ the lone pair is least available due to stronger resonance/electron-withdrawing influence.

Thus basic strength decreases as: $(B) > (D) > (A) > (C)$

4. Convert to increasing order of $pK_b$

Since stronger base $\Rightarrow$ smaller $pK_b$,

$\text{increasing } pK_b : (B) < (D) < (A) < (C)$

5. Match with options

This corresponds to Option C.

6. Comparison with stored correct answer

Stored correct answer = C

Derived answer = C

So they agree.