
To determine the number of aromatic compounds, we must check each structure for aromaticity criteria: cyclic, planar, fully conjugated, and follows Huckel’s rule (4n+2 π electrons).
Count of aromatic compounds: (A), (C), (D) = 3.
Compounds B, C, and D are aromatic. Aromatic compounds must follow Huckel’s rule (\(4n + 2\) electrons) and have a planar, conjugated structure. Compound A is not aromatic as it does not satisfy these criteria.
The correct increasing order of stability of the complexes based on \( \Delta \) value is:
Match List-I with List-II: List-I



For the circuit shown above, the equivalent gate is:
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: