Consider the following molecule (X).
The Structure X is? 




The given molecule (X) visually appears to have a bicyclic structure with two fused rings. It consists of one five-membered ring fused with a six-membered ring. Let's analyze the structure and find the correct identification.
Step-by-Step Solution:
Hence, the structure (X) is Indene.
The correct answer is option 2, which correctly represents the structure of indene.
This identification relies on recognizing the common fused ring systems and their structural characteristics in organic chemistry.
To identify the structure of molecule (X), we need to analyze its structural features. The molecule consists of two fused rings: a five-membered ring and a six-membered ring. This characteristic is typical of bicyclic aromatic compounds.
Given the structure, the molecule resembles naphthalene, but with an additional methylene bridge connecting the two rings. This specific arrangement indicates that the molecule is an example of Indene.
Let's examine the options provided:
The correct answer is the structure that matches the indene configuration:
Conclusion: Hence, the structure of molecule (X) is indene. The correct option is the one which accurately represents the indene structure, consistent with the analysis conducted.

How many different stereoisomers are possible for the given molecule? 
Which of the following is true for the stereochemical relationship of the given structures (A-D)?

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: