Final answer:
The cell with a mutation in potassium channels will swell and potentially burst due to an increase in internal osmolarity and water influx via active aquaporins, resulting in a hypotonic state with increased osmolarity inside the cell.
Step-by-step explanation:
If a cell develops a mutation in its potassium channels that prevents potassium ions from leaving the cell, the internal concentration of ions within the cell will increase. This leads to an increase in osmolarity of the cell's interior compared to the extracellular fluid. Since aquaporins are still active, water will move into the cell to balance this concentration difference through osmosis. As a result, the cell will be in a hypotonic state, where there is a lower concentration of solutes outside than inside the cell, and will swell due to the influx of water. If this process continues without regulation, the cell may eventually burst due to the excessive internal pressure. Thus, the correct answer is: d) Cell will burst; hypotonic, increased osmolarity.