Explanation:

Introduction:
In order to determine whether a molecule is chiral or achiral, we need to analyze its symmetry elements and determine if any of them are present. A molecule is considered achiral if it possesses a symmetry element that allows it to be superimposed on its mirror image. In other words, an achiral molecule is one that is indistinguishable from its mirror image.

Symmetry Elements:
There are several symmetry elements that can exist in a molecule, including a centre of symmetry, a plane of symmetry, and an axis of symmetry.

A centre of symmetry:
A molecule possesses a centre of symmetry (also known as an inversion center) if there is a point in the molecule's structure where each atom has an identical atom located an equal distance from the center but in the opposite direction. This symmetry element allows a molecule to be superimposable on its mirror image.

A plane of symmetry:
A molecule possesses a plane of symmetry if there is a plane that divides the molecule into two halves that are mirror images of each other. This symmetry element allows a molecule to be superimposable on its mirror image.

A C2 axis of symmetry:
A molecule possesses a C2 axis of symmetry if there is a rotation axis that passes through the molecule and rotates it by 180 degrees, resulting in an identical structure. This symmetry element does not necessarily allow a molecule to be superimposable on its mirror image.

Analysis of 2-methylpent-2,3-diene:
In the case of 2-methylpent-2,3-diene, there is no centre of symmetry present in the molecule. Each atom does not have an identical atom located an equal distance from the center but in the opposite direction.

However, there is a plane of symmetry present in the molecule. If we draw a plane that bisects the molecule, we can see that the two halves are mirror images of each other. This plane of symmetry allows the molecule to be superimposable on its mirror image.

Conclusion:
Based on the analysis of the symmetry elements in 2-methylpent-2,3-diene, we can conclude that it is achiral because it possesses a plane of symmetry. Therefore, the correct answer is (b) - it has a plane of symmetry.

C