To answer this question about nucleophilic substitution reactions in chiral alkyl halides, let's first understand the two types of nucleophilic substitution reactions: \( SN_1 \) and \( SN_2 \).
Now, let's evaluate the given options:
Thus, the correct statement is: Racemisation occurs in \( S_N1 \) reaction and inversion occurs in \( S_N2 \) reaction.
- SN1 Reaction: This reaction proceeds via a carbocation intermediate, leading to a racemic mixture if the carbon is chiral, due to the planar nature of the carbocation.
- SN2 Reaction: This reaction involves a backside attack, resulting in inversion of configuration (Walden inversion) if the carbon is chiral.
Thus, racemisation occurs in SN1 reactions and inversion occurs in SN2 reactions.


Let \( f : \mathbb{R} \to \mathbb{R} \) be a twice differentiable function such that \[ (\sin x \cos y)(f(2x + 2y) - f(2x - 2y)) = (\cos x \sin y)(f(2x + 2y) + f(2x - 2y)), \] for all \( x, y \in \mathbb{R}. \)
If \( f'(0) = \frac{1}{2} \), then the value of \( 24f''\left( \frac{5\pi}{3} \right) \) is: