The preferred conformation or Cis -3-tert - buty1-1- methyl cyclohexane is the one in which: . A) the tert-butyl group is axial and the methyl group is equatorial.
B) the methyl group is axial and the tert-butyl group is equatorial.
C) both groups are axial.
D) both groups are equatorial.
E) the molecule exists in a boat conformation.

D) both groups are equatorial.

Explanation:

To solve this question we can start by drawing the molecule in using the structure of the hexagon. In this structure, we have the methyl group on carbon 1 and the terbutyl group on carbon 3, additionally, if we have a cis structure both groups must have the same type of bond (in this case the wedge bond).  (See figure 1)

When we write the chair structure, we must keep the same structure. That is, methyl must be on carbon 1 and terbutyl on carbon 3. Also, the cis configuration must be maintained. With this in mind, we can choose the equatorial configuration for methyl on carbon 1 (since the position equatorial is the one that has less steric impediment and more stability). If this is true for carbon 1, we must place the terbutyl group on carbon 3 in the same configuration (i.e. cis). Therefore, on carbon 3 we must place the tert-butyl down on carbon 3, that is, in the equatorial position.  (See figure 1).

Therefore, in the chair-like structure, both groups must be in an equatorial position.

I hope it helps!