Final answer:
Option (b) export of Ca2+ from the cytosol and option (d) export of Na+ from cells to maintain resting membrane potential occur without coupling transport to the movement of a second solute, as both processes use independent active transport mechanisms such as ATPase pumps.
Step-by-step explanation:
The question explores the process by which different substances are transported across the cell membrane, particularly focusing on ways that do not require the coupling transport of a solute to the movement of another solute.
Among the options provided, the import of glucose into gut epithelial cells (a), and the export of H+ from animal cells for pH regulation (c) generally involve coupled or secondary active transport.
During the import of glucose in gut epithelial cells, a symporter carries both glucose and Na+ into the cell using the gradient established by a Na+/K+ ATPase pump, while the export of H+ often occurs through antiporters or symporters where the movement of H+ is coupled with another ion.
On the other hand, the export of Ca2+ from the cytosol (option b) often uses an independent active transport mechanism like the Ca2+ ATPase pump, which actively pumps calcium ions out of cells without coupling with another solute.
Similarly, the export of Na+ from cells to maintain a resting membrane potential (option d) typically involves the Na+/K+ ATPase pump, which actively transports Na+ out and K+ in without coupling their movement to another solute directly.
In summary, the processes that occur without coupling transport of the solute to the movement of a second solute are the export of Ca2+ from the cytosol and the export of Na+ from cells to maintain resting membrane potential.
Therefore, the correct options that answer the question are (b) export of Ca2+ from the cytosol and (d) export of Na+ from cells to maintain resting membrane potential.