To determine the number of geometrical isomers for the given structure:
Identifying Stereocenters: The given structure contains three stereocenters, which influence the overall geometric configurations.
Counting Geometrical Isomers: The maximum potential geometric isomers can be calculated using the formula:
Total Geometrical Isomers = 2n
where n is the number of stereocenters. In this case:
23 = 8
However, due to symmetry in the molecule, some configurations are equivalent, reducing the number of unique geometrical isomers.
Final Count: Considering the symmetry and equivalent configurations, the total number of unique geometrical isomers for the given structure is 4.
The incorrect statements regarding geometrical isomerism are:
(A) Propene shows geometrical isomerism.
(B) Trans isomer has identical atoms/groups on the opposite sides of the double bond.
(C) Cis-but-2-ene has higher dipole moment than trans-but-2-ene.
(D) 2-methylbut-2-ene shows two geometrical isomers.
(E) Trans-isomer has lower melting point than cis isomer.
Given below are two statements:
Statement (I):
are isomeric compounds.
Statement (II): are functional group isomers.
In the light of the above statements, choose the correct answer from the options given below:
Let \( y = f(x) \) be the solution of the differential equation
\[ \frac{dy}{dx} + 3y \tan^2 x + 3y = \sec^2 x \]
such that \( f(0) = \frac{e^3}{3} + 1 \), then \( f\left( \frac{\pi}{4} \right) \) is equal to:
Find the IUPAC name of the compound.
If \( \lim_{x \to 0} \left( \frac{\tan x}{x} \right)^{\frac{1}{x^2}} = p \), then \( 96 \ln p \) is: 32