



Step 1: When sec-butylcyclohexane reacts with bromine in the presence of sunlight, a free radical substitution reaction occurs.
Step 2: In this reaction, the bromine atom will substitute one of the hydrogen atoms at the benzylic position of sec-butylcyclohexane. The benzylic hydrogen is the most reactive in this case due to the stability of the resulting free radical formed by the abstraction of the hydrogen atom.
Step 3: Therefore, the major product will have a bromine atom attached to the carbon atom adjacent to the cyclohexane ring, which is the sec-butyl position.

For \( \alpha, \beta, \gamma \in \mathbb{R} \), if \[ \lim_{x \to 0} \frac{x^2 \sin(\alpha x) + (\gamma - 1)e^{x^2}}{\sin(2x - \beta x)} = 3, \] then \( \beta + \gamma - \alpha \) is equal to:

In the first configuration (1) as shown in the figure, four identical charges \( q_0 \) are kept at the corners A, B, C and D of square of side length \( a \). In the second configuration (2), the same charges are shifted to mid points C, E, H, and F of the square. If \( K = \frac{1}{4\pi \epsilon_0} \), the difference between the potential energies of configuration (2) and (1) is given by: