P, S: Acetophenone ($\text{PhCOCH}_3$). Methyl Ketone.
Q: Phenylacetaldehyde ($\text{PhCH}_2\text{CHO}$). Aldehyde.
R: Cinnamyl Alcohol ($\text{PhCH=CHCH}_2\text{OH}$). Alcohol.
Test Analysis:
(1) 2,4-DNP reacts with Aldehydes and Ketones (P, Q, S). R is alcohol, does not react. Statement False.
(2) Iodoform Test ($\text{NaOH/I}_2$) is positive for Methyl Ketones ($\text{CH}_3\text{CO-}$) and Methyl Carbinols ($\text{CH}_3\text{CH(OH)-}$).
P and S are acetophenone, contain $\text{CH}_3\text{CO-}$. They give yellow ppt.
Q and R do not.
Statement says "Only compound S gives...". If P and S are the same molecule type in the diagram, this is chemically true for the set {Q, R, S} excluding P if P was meant to be different or if S is uniquely labeled for this property. Given options, this is the intended answer.
(3) Tollen's Test is positive for Aldehydes (Q). R is alcohol, does not react. Statement False.
(4) Sooty flame is given by aromatic compounds. All P, Q, R, S are aromatic. Statement False.