List-I Compound | List-II Product in Basic Medium (in NaOH + Heat) | ||
A | Ethanal | (I) | Benzoic acid + Phenyl methanol |
B | Methanal | (II) | 3-Hydroxybutanal + But-2-enal |
C | Benzenecarbaldehyde | (III) | 4-Hydroxy-4-methylpentan-2-one + 4-Methylpent-3-en-2-one |
D | Acetone | (IV) | Formic acid + Methanol |
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