Step 1: State the rule for nucleophilic addition. Reactivity towards nucleophilic addition rises as the carbonyl carbon becomes more positive (more electrophilic). More positive charge means an easier attack by the nucleophile. Step 2: Place the ketone lowest. Benzophenone (a) is a ketone with two bulky phenyl groups. These cause steric crowding and push electron density onto the carbonyl carbon, so it is the least reactive. Step 3: Compare the methyl substituted aldehyde. In $p$-methylbenzaldehyde (b) the $-CH_3$ group donates electrons, slightly lowering the positive charge on the carbonyl carbon, so it is less reactive than plain benzaldehyde. Step 4: Position benzaldehyde. Benzaldehyde (c) has no donating or withdrawing substituent, so it is more reactive than the methyl substituted one. Step 5: Place the nitro substituted aldehyde highest. In $p$-nitrobenzaldehyde (d) the strongly electron withdrawing $-NO_2$ group raises the positive charge on the carbonyl carbon, making it the most reactive. Step 6: Write the increasing order. Putting these together gives $a < b < c < d$, which is option 1. \[ \boxed{a < b < c < d} \]
