The IUPAC name of the following compound is:

The problem asks for the IUPAC name of the given compound. To determine the correct name, we'll perform a step-by-step analysis based on IUPAC nomenclature rules:
Thus, the correct IUPAC name of the compound is "Hept-1-en-6-yn-4-ol."
Explanation of other options:
To determine the IUPAC name of the given compound, we will follow standard nomenclature rules:
Justification of options:
4-Hydroxyhept-1-en-6-yne
4-Hydroxyhept-6-en-1-yne
Hept-6-en-1-yn-4-ol
Hept-1-en-6-yn-4-ol
Match List - I with List - II: 
Choose the correct answer from the given below options
Which of the following is the correct IUPAC name of the given organic compound (X)?
The structure of compound $ X $ is as follows:
$ \text{H}_3\text{C} - \text{CH}_3 - \text{CH} = \text{CH} - \text{H} - \text{Br} $


For the circuit shown above, the equivalent gate is:
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: