For cis-1 3-dimethylcyclohexane which two chair conformations are in equilibrium

D & E

Explanation:

The chair conformations must have a "down-down" or "up-up" relationship.

As we know the geometry about sp³ hybridized carbon is tetrahedral. In case of cyclohexanes the overall molecule is not flat as often we sketch it on our notebooks. In real sense, the cyclohexanes adopts two conformations; a boat conformation and a chair conformation. The boat conformation feels some what greater sterric hindrance so it is less often found while the chair conformation is very stable hence it is favored.

Below the figure shows the chair conformations of cis-1 3-dimethylcyclohexane. Also, cis-1 3-dimethylcyclohexane exists in two chair form because conformations are also referred to those compounds which are continuously changing its form and is in dynamic state. Also conformations are temperature dependent. That is why cyclohexanes give different peaks in H-NMR at chilling temperatures and normal temperatures.

On close look up on cyclohexane we found that the twelve substituents are not the same. But, 6 substituents occupy axial positions while the remaining six substituents adopts the equatorial positions.

Below figure shows the the conformations of cis-1 3-dimethylcyclohexane which are dynamic and in equilibrium.