The increasing order of the rate of HCN addition to compounds A - D is (A) HCHO (B) $$CH_3COCH_3$$ (C) $$PhCOCH_3$$ (D) PhCOPh

Nucleophilic addition of $$HCN$$ to a carbonyl group depends mainly on two factors:
  1. Electronic factor - the electron density on the carbonyl carbon. Electron-releasing groups (+I) and conjugation with an aromatic ring decrease the electrophilicity of the carbonyl carbon, so the rate falls.
  2. Steric factor - bulky groups around the carbonyl carbon hinder the approach of the nucleophile $$CN^-$$, again lowering the rate.

Let us analyse each compound.

Case A : HCHO (formaldehyde)
Both substituents are hydrogen. Hydrogen shows neither +I nor steric hindrance, so the carbonyl carbon is highly electrophilic and easily attacked. Hence, formaldehyde is the MOST reactive.

Case B : $$CH_3COCH_3$$ (acetone)
Each methyl group exerts a +I effect that pushes electron density toward the carbonyl carbon, decreasing its positive character. Some steric hindrance is also present. Therefore, acetone is less reactive than formaldehyde.

Case C : $$PhCOCH_3$$ (acetophenone)
One substituent is phenyl. In addition to the +I effect of the methyl group, the phenyl ring is conjugated with the carbonyl: $$Ph{-}C\! =\! O \leftrightarrow Ph{-}C^{+}{-}O^-$$. This resonance delocalises the positive charge away from the carbonyl carbon, further reducing electrophilicity. Steric crowding is also larger than in acetone. Hence, acetophenone is less reactive than acetone.

Case D : $$PhCOPh$$ (benzophenone)
Both substituents are phenyl rings. Conjugation with two aromatic rings strongly withdraws the positive charge from the carbonyl carbon, and the steric bulk is the greatest. Consequently, benzophenone is the LEAST reactive toward $$HCN$$ addition.

Combining all observations, the rates of addition follow the order
$$PhCOPh \; (D) \; \lt \; PhCOCH_3 \; (C) \; \lt \; CH_3COCH_3 \; (B) \; \lt \; HCHO \; (A)$$

Thus, the increasing order is
$$D \lt C \lt B \lt A$$

Option C which is: D < C < B < A