Given,
1. "A" forms an Orange colour precipitate with 2,4 Dinitrophenylhydrazine. It means that A is an aldehyde or Ketone.
2. It is given that A gives iodoform test, so it must have CH3−CO group.
3. Also given " A" does not reduce Tollen or Fehling's reagent.
⇒ A must be a ketone.
4. Given A has molecular formula C8H8O
⇒ A is unsaturated, but also given A doesn't decolorize bromine water ort Bayer's reagent
⇒ A is unsaturated, having benzene ring.
5. It is given that "A" on drastic oxidation changes to carboxylic acid "B".
As A is a ketone B will have one less carbon than A
⇒ A can be C6H5−COCH3
6. Also, a Total number of carbon atoms given in A are 8,[C8H8O]
⇒ A is acetophenone [C6H5−CO−CH3]
7. Molecular formula of B is C7H6O2
⇒ B is Benzoic acid.
∴ A is Acetophenone, B is Benzoic Acid.