This is an excellent question, probably the best in the paper. Pyrolysis of peroxyesters is not conventionally taught anywhere for IIT-JEE preparation, not even in any standard organic chemistry course. But the question is throughly logical. It can be answered after a bit of reflection by anyone with good basics of reaction mechanism.

Four pathways for reactions are given :

Note that first homolytic fission is expected to give + R'O ∙ . This is usually unstable (remember kolbe's electrolysis) and decomposes to R ∙ + CO 2 . But is stable, since it is a difficult bond to break. Hence in (1) & (3), which have groups, Ph–CH 2 ∙ will be formed (  benzyl radical is stable) so P or Q are possible pothways for them. For (2 & 4), R & S pathways will be more likely.

∴ 1: P or Q 2 : R or S

2: P or Q 4 : R or S

Now consider R'O ∙ . If it is CH 3 O ∙ , It cannot splite.

But ⎯→ + can occur. Hence carbonyl compound will be formed with 3 & 4, but not with 1 & 2.

∴ 1 : P or S 3 : Q or R

2 : P or S 4 : Q or R

combining these options gives : 1 : P , 2 : S, 3 : Q , 4 : R

I cannot but help commenting that such questions are those which make IIT-JEE what it is. A good motivation for students to keep thinking while studying.