1. Use the relation between basic strength and $\mathrm{p}K_b$

For amines:

• Stronger base $\Rightarrow$ smaller $\mathrm{p}K_b$
• Weaker base $\Rightarrow$ larger $\mathrm{p}K_b$

Given values in List II are: $3.25,\ 3.00,\ 9.38,\ 3.29$

Clearly, $9.38$ is much larger than the others, so it must correspond to the weakest base.

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2. Identify the weakest base

A. Aniline

Aniline is an aromatic amine. The lone pair on nitrogen is involved in resonance with the benzene ring: $\ce{C6H5-NH2}$ Because of delocalization, the lone pair is less available for protonation, so aniline is much less basic than aliphatic amines.

Therefore: $\text{A. Aniline} \to \mathrm{p}K_b = 9.38 \quad (\text{III})$

So, $A \to III$

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3. Compare the aliphatic amines

The remaining compounds are:

• B. Ethanamine (primary amine)
• C. N-Ethylethanamine (secondary amine)
• D. N,N-Diethylethanamine (tertiary amine)

In aqueous solution, basic strength of lower aliphatic amines generally follows: $2^\circ > 1^\circ > 3^\circ$ This is due to a balance of:

• $+I$ effect increasing electron density on nitrogen
• solvation of the conjugate acid

Thus among these three:

• Secondary amine is strongest base $\Rightarrow$ smallest $\mathrm{p}K_b$
• Primary amine is next
• Tertiary amine is slightly weaker than primary in water

So the order is: $\text{C} > \text{B} > \text{D}$

Hence the $\mathrm{p}K_b$ order should be: $\text{C} < \text{B} < \text{D}$

Among the remaining values: $3.00 < 3.25 < 3.29$

Therefore:

• C $\to 3.00$ (II)
• B $\to 3.25$ (I) or $3.29$ (IV)?
• D $\to 3.29$ (IV) or $3.25$ (I)?

Using known approximate values:

• Ethylamine: $\mathrm{p}K_b \approx 3.25$
• Diethylamine: $\mathrm{p}K_b \approx 3.0$
• Triethylamine: $\mathrm{p}K_b \approx 3.29$

So: $B \to I, \quad C \to II, \quad D \to IV$

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4. Final matching

Thus the correct match is:

• $A \to III$
• $B \to I$
• $C \to II$
• $D \to IV$

So the full answer is: $A\text{-}III,\ B\text{-}I,\ C\text{-}II,\ D\text{-}IV$

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5. Compare with given options

Options given are:

• A: $A$-III, $B$-II, $C$-I, $D$-IV
• B: $A$-III, $B$-II, $C$-IV, $D$-I
• C: $A$-III, $B$-IV, $C$-II, $D$-I
• D: $A$-I, $B$-IV, $C$-II, $D$-III

The exact correct matching we derived is not present in the options.

Among standard textbook values, the correct mapping should be: $A\text{-}III,\ B\text{-}I,\ C\text{-}II,\ D\text{-}IV$

So the stored answer C does not agree with the chemically correct order.

It appears the option set may contain a misprint/interchange in the values for ethanamine and triethylamine.