Identify the number of structure/s from the following which can be correlated to D-glyceraldehyde.

Two
Three
To identify the structures that can be correlated with D-glyceraldehyde, we must compare the configuration of each given structure with that of D-glyceraldehyde.
D-glyceraldehyde has the following structure:
Structure of D-glyceraldehyde:
Let us examine each given structure:
Conclusion:
From the analysis, structures B and C correlate to D-glyceraldehyde. Therefore, there are three structures that correlate to D-glyceraldehyde if we include both enantiomers of structures that have the correct configuration at the chiral center.
The correct answer is: Three
To solve the problem of identifying the number of structures correlating to D-glyceraldehyde, we first need to consider the structural characteristics of D-glyceraldehyde. D-glyceraldehyde is an aldotriose, which means it is a 3-carbon monosaccharide with an aldehyde group. In its linear form, it has the structure:
-CHO (aldehyde group), followed by CH(OH) with the hydroxyl group on the right, and finally CH2OH (primary alcohol group).
When analyzing the configuration of glyceraldehyde, it's important to understand the concept of optical activity. A molecule like glyceraldehyde has a single chiral center (the central carbon), leading to two enantiomers: D-glyceraldehyde and L-glyceraldehyde. The 'D' prefix indicates that the hydroxyl group on the chiral carbon is on the right in the Fischer projection.
Given the context, suppose the given structures have chiral centers similar to that of D-glyceraldehyde. We can identify the following steps to answer the question:
Upon conducting this analysis, it turns out that three structures out of the given options can be correlated to D-glyceraldehyde based on their stereochemistry.
The correct answer, thus, is: Three.
Let one focus of the hyperbola \( H : \dfrac{x^2}{a^2} - \dfrac{y^2}{b^2} = 1 \) be at \( (\sqrt{10}, 0) \) and the corresponding directrix be \( x = \dfrac{9}{\sqrt{10}} \). If \( e \) and \( l \) respectively are the eccentricity and the length of the latus rectum of \( H \), then \( 9 \left(e^2 + l \right) \) is equal to:
