Write the formula to calculate the specific rotation of an optically active compound.

For the given compound X, the total number of optically active stereoisomers is ____.

Represent the union of two sets by Venn diagram for each of the following.

$X=\{x | x$ is a prime number between $80$ and $100\}$

$Y=\{y | y$ is an odd number between $90$ and $100\}$

Trans-3,6-Dimethyl oct-4-ene (A) exists in two diastereomers $\left(\text{I}\right)$ and $\left(\text{II}\right)$.



Which statements is true about $\left(\text{I}\right)$ and $\left(\text{II}\right)$ ?

(+) - mandelic acid has a specific rotation of 158^o. What would be the observed specific rotation of a mixture of 25% (-) - mandelic acid and 75% (+) - mandelic acid ?