Final answer:
In the Barrovian sequence, Kyanite and Sillimanite would not be expected to coexist in the same rock due to their formation under different temperature and pressure conditions in metamorphic rocks.
Step-by-step explanation:
Based on the Barrovian sequence of index minerals, the pair of minerals you would not expect to find in the same rock is Kyanite and Sillimanite. These minerals, along with andalusite, are polymorphs of Al2SiO5, meaning they have the same chemical composition but different crystal structures and form under different temperature and pressure conditions in metamorphic rocks.
The rocks that typically contain these index minerals can tell us about the pressure-temperature conditions of their formation. For instance, rocks with kyanite and sillimanite are indicative of medium-pressure terranes often associated with continent-continent collision zones.