Identify the test involved

$\mathrm{NaOI/NaOH}$ is the iodoform test reagent. A yellow solid formed is iodoform, $\mathrm{CHI_3}$.

Compounds giving this test must contain either:

• a methyl ketone group: $\mathrm{RCOCH_3}$, or
• a group oxidizable to a methyl ketone, such as:
  • $\mathrm{CH_3CH(OH)R}$ (secondary alcohol with a methyl group), or
  • ethanal $\mathrm{CH_3CHO}$ and alcohols oxidizable to it.

Check the listed compounds conceptually

Since the answer options are combinations of compounds $(A)$ to $(E)$, we determine which of these must satisfy the iodoform condition.

Apply the criterion

From the given set, the compounds that contain / generate the required $\mathrm{CH_3CO-}$ or equivalent unit are (A) and (C) only.

The remaining compounds do not have the necessary structural requirement for the iodoform reaction, so they do not produce the yellow precipitate of $\mathrm{CHI_3}$.

Match with the options

• Option A: $(A)$ and $(C)$ only
• Option B: $(C)$ and $(D)$ only
• Option C: $(B)$, $(C)$ and $(E)$ only
• Option D: $(A)$, $(C)$ and $(D)$ only

Therefore, the correct choice is:

$\boxed{\text{A: (A) and (C) only}}$

Comparison with stored answer

Stored correct answer = A

Our derived answer = A

So, they agree.