Step 1: Observe the common terpene framework.
All the given structures are acyclic monoterpene-type moleculesThey contain two isoprene units and have carbon-carbon double bonds at different relative positions
Step 2: Analyze ozonolysis products.
Ozonolysis cleaves carbon-carbon double bonds and converts the alkene carbons into carbonyl compoundsSince all the given terpenes contain a common substituted alkene fragment, cleavage of that part gives at least one identical carbonyl compound
Step 3: Check statement (A).
Because all four terpenes have a common alkene portion, their ozonolysis gives at least one common carbonyl productTherefore, statement (A) is correct
Step 4: Compare terpenes N and O.
Terpenes N and O have the same molecular formula and same connectivityThey differ only in the spatial arrangement around a carbon-carbon double bondThus, they are geometrical isomers
Step 5: Check statement (B).
Since N and O differ only as E/Z forms around the double bond, statement (B) is correct
Step 6: Analyze Diels-Alder possibility for terpene O.
Terpene O contains a conjugated diene systemA conjugated diene can undergo Diels-Alder reaction with an electron-poor dienophile such as maleic anhydrideTherefore, statement (C), which says that O cannot undergo Diels-Alder reaction, is incorrect
Step 7: Compare $\lambda_{\max}$ values.
$\lambda_{\max}$ for $\pi-\pi^*$ absorption increases with conjugationTerpene P has the least effective conjugation among the given structures, so it absorbs at the lowest wavelengthHence, statement (D) is correct
\[
\boxed{\text{(A), (B) and (D)}}
\]