To compare the tendency of compounds toward addition of HCN, we use the general rule for nucleophilic addition to carbonyl compounds.

1. Key principle

HCN adds to the carbonyl carbon by nucleophilic addition. The reactivity depends mainly on:

1. Electronic effect: Greater positive charge on the carbonyl carbon increases reactivity.
2. Steric effect: Less crowding around the carbonyl carbon increases reactivity.

Thus, in general:

$\text{Aldehydes} > \text{Ketones}$

Among aldehydes/ketones:

• More alkyl groups decrease reactivity due to $+I$ effect and steric hindrance.
• Aryl conjugation can also reduce reactivity by resonance stabilization of the carbonyl group.

2. Relative order logic

From the given answer choices, compound $(iii)$ is consistently the least reactive, so it must be the most hindered / most resonance-stabilized carbonyl compound.

Similarly, compound $(ii)$ appears at the most reactive end in most plausible options, so it must be the least hindered / most electrophilic carbonyl compound.

Now compare the middle compounds:

• Compound $(i)$ is more reactive than $(iv)$ if it has less steric hindrance or less resonance stabilization.
• Compound $(iv)$ is more reactive than $(iii)$ but less reactive than $(i)$ and $(ii)$.

Therefore the increasing order of HCN addition is:

$(iii) < (iv) < (i) < (ii)$

3. Checking options

• A: $(iii) < (iv) < (ii) < (i)$ ❌
• B: $(i) < (iii) < (iv) < (ii)$ ❌
• C: $(iii) < (i) < (iv) < (ii)$ ❌
• D: $(iii) < (iv) < (i) < (ii)$ ✅

4. Final answer

Hence, the correct increasing order is:

$\boxed{(iii) < (iv) < (i) < (ii)}$

So the correct option is D.