The observations for each test are:
A: Br$_2$ water test indicates unsaturation (reddish orange color disappears).
B: Ceric ammonium nitrate test detects alcohols (red color appears).
C: Ferric chloride test detects phenols (blue, green, violet, or red color appears).
D: 2,4-DNP test detects aldehydes/ketones (yellow-orange precipitate).
Match List I with List II.
In which of the following reactions of H$_2$O$_2$ acts as an oxidizing agent (either in acidic, alkaline, or neutral medium)?
% Given Reactions
(i) \( 2Fe^{2+} + H_2O_2 \rightarrow \)
(ii) \( 2MnO_4^- + 6H^+ + 5H_2O_2 \rightarrow \)
(iii) \( I_2 + H_2O_2 + 2OH^- \rightarrow \)
(iv) \( Mn^{2+} + H_2O_2 \rightarrow \)
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