To identify aromaticity:
1. Check for a cyclic, planar structure.
2. Count π-electrons in the conjugated system.
3. Verify if it follows \(4n + 2\) rule (\(n = 0, 1, 2,...\)).
Only option (a) lacks aromaticity.
Thus, the correct answer is \(\boxed{1}\).
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Approach Solution -2
Step 1: Understand Hückel's rule for aromaticity.
A compound is aromatic if it is cyclic, planar, fully conjugated, and contains \((4n + 2)\) \(\pi\)-electrons, where \(n\) is a non-negative integer.
Step 2: Analyze each compound.
(a) Cyclohexa-1,3-diene: It has 4 \(\pi\)-electrons (from two double bonds), which does not satisfy Hückel's rule (\(4n + 2\)). Therefore, it is non-aromatic.
(b) Benzene: It has 6 \(\pi\)-electrons, satisfying Hückel's rule with \(n=1\). It is aromatic.
(c) Cyclopentadienyl anion: It has 6 \(\pi\)-electrons (4 from double bonds plus 2 from the lone pair on the negatively charged carbon), satisfying Hückel's rule. It is aromatic.
(d) Tropylium cation: It has 6 \(\pi\)-electrons in a planar cyclic conjugated system, satisfying Hückel's rule. It is aromatic.
Step 3: Conclusion.
Only option (a) — cyclohexa-1,3-diene — is non-aromatic.
Hence, the correct answer is \(\boxed{1}\).