• 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.
Let \( y = f(x) \) be the solution of the differential equation
\[ \frac{dy}{dx} + 3y \tan^2 x + 3y = \sec^2 x \]
such that \( f(0) = \frac{e^3}{3} + 1 \), then \( f\left( \frac{\pi}{4} \right) \) is equal to:
Find the IUPAC name of the compound.
If \( \lim_{x \to 0} \left( \frac{\tan x}{x} \right)^{\frac{1}{x^2}} = p \), then \( 96 \ln p \) is: 32