The reaction involved is an aldol condensation reaction. The mechanism is as follows:
The product is formed by the reaction of two molecules of benzaldehyde (PhCHO) and one molecule of acetone (CH$_3$COCH$_3$) in the presence of alkali and heat.
The reaction involves the removal of water (H$_2$O) through dehydration, leading to the formation of a conjugated system.
The major product contains:
-3 double bonds in the benzene ring (Ph),
-2 double bonds formed during the aldol reaction,
-carbonyl (C = O) group in the product.
Total $\pi$-bonds = 9.
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