Step 1: Revisiting pericyclic reaction rules.
Woodward–Hoffmann rules determine whether cycloadditions are photochemically or thermally allowed.
[4$\pi$ + 2$\pi$] → thermally allowed (Diels–Alder).
[2$\pi$ + 2$\pi$] → photochemically allowed.
Step 2: Checking each statement.
(A) Incorrect → [4$\pi$ + 2$\pi$] occurs thermally, not photochemically.
(B) Correct → [2$\pi$ + 2$\pi$] is photochemically allowed.
(C) Correct → Diels–Alder is a classic thermally allowed reaction.
(D) Incorrect → Only s-cis dienes undergo Diels–Alder; transoid (s-trans) can’t cyclize.
Step 3: Conclusion.
Thus, the incorrect statements are (A) and (D).