Explanation:
1. Assertion (A): Correct. - In \( C_6H_5CH_2Br \), the \( CH_2-Br \) bond is connected to a benzyl group. The phenyl ring allows for stabilization of the transition state via resonance, facilitating the \( S_N2 \) reaction. This makes the reaction proceed more readily compared to \( CH_3CH_2Br \), where no such stabilization exists.
2. Reason (R): Correct. - The unhybridized \( p \)-orbital formed during the trigonal bipyramidal transition state interacts with the conjugated system of the phenyl ring, providing extra stabilization.
3. Conclusion: Both (A) and (R) are correct, and (R) is the correct explanation for (A).
Final Answer is option (3).
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: