To determine which statements are correct, let's evaluate each one based on chemical principles:
After evaluating each statement, the correct answer is: A, C, D only.
• A: True. Glycerol decomposes at its normal boiling point, so it is purified by vacuum distillation.
• B: False. Aniline is immiscible in water but can still be purified by steam distillation.
• C: True. Ethanol forms an azeotrope with water, making azeotropic distillation effective for separation.
• D: True. A pure organic compound exhibits the same melting point even when mixed with another sample of the same compound.
Match the Compounds (List - I) with the appropriate Catalyst/Reagents (List - II) for their reduction into corresponding amines. 
Consider the following amino acid: 
Which of the following options contain the correct structure of (A) and (B)?
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: