Hydrolysis of molecules depends on the leaving group and the electrophilicity of the carbonyl carbon. The best leaving group in this case is the chloride ion (Cl-), which is a strong leaving group. Methyl chloride (option 1) contains a chlorine atom bonded to a methyl group, making it a good candidate for fast hydrolysis under basic conditions. In comparison, acetamide (option 2) has an amine group which is not a good leaving group, methyl acetate (option 3) contains an ester group but the leaving group is relatively less reactive, and ethyl formate (option 4) contains an ester group as well, but it is less reactive than methyl chloride. Therefore, methyl chloride undergoes hydrolysis the fastest.
If \[ \frac{dy}{dx} + 2y \sec^2 x = 2 \sec^2 x + 3 \tan x \cdot \sec^2 x \] and
and \( f(0) = \frac{5}{4} \), then the value of \[ 12 \left( y \left( \frac{\pi}{4} \right) - \frac{1}{e^2} \right) \] equals to: