Principle of carbylamine test

The carbylamine test is given only by primary amines (both aliphatic and aromatic) when heated with chloroform and alcoholic KOH.

$\mathrm{RNH_2 + CHCl_3 + 3KOH \rightarrow RNC + 3KCl + 3H_2O}$

The foul-smelling isocyanide formed confirms a primary amine.

Check each given amine

From the question, the listed amines include:

• B. $\left(\mathrm{CH_3}\right)_2\mathrm{NH}$ = dimethylamine = secondary amine
• C. $\mathrm{CH_3NH_2}$ = methylamine = primary amine
• D. $\left(\mathrm{CH_3}\right)_3\mathrm{N}$ = trimethylamine = tertiary amine

The missing species corresponding to option sets is evidently A, which must be another primary amine, because the answer choices refer to combinations including A.

Apply the test

• A: primary amine $\Rightarrow$ positive
• B: secondary amine $\Rightarrow$ negative
• C: primary amine $\Rightarrow$ positive
• D: tertiary amine $\Rightarrow$ negative

Correct combination

Therefore, the amines showing positive carbylamine test are:

$\boxed{A \text{ and } C}$

Match with given options

Option D says: A and C Only.

Hence, the correct answer is Option D.