The compound with molecular formula C\(_6\)H\(_6\), which gives only one monobromo derivative and takes up four moles of hydrogen per mole for complete hydrogenation has ___ \(\pi\) electrons.
Designate whether each of the following compounds is aromatic or not aromatic.

Conc. HNO\(_3\)
Find the IUPAC name of the compound.

Let \( f : \mathbb{R} \to \mathbb{R} \) be a twice differentiable function such that \[ (\sin x \cos y)(f(2x + 2y) - f(2x - 2y)) = (\cos x \sin y)(f(2x + 2y) + f(2x - 2y)), \] for all \( x, y \in \mathbb{R}. \)
If \( f'(0) = \frac{1}{2} \), then the value of \( 24f''\left( \frac{5\pi}{3} \right) \) is: