Cellulose is a polymer of glucose linked by beta (1-4) linkages. Humans lack the enzyme that catalyzes the cleavage of this bond; thus cellulose (dietary fiber) is indigestible and passes through the digestive system unchanged.

Only small, nonpolar molecules can freely diffuse through the plasma membrane. From this group, only oxygen fits this description. Hydrogen and potassium ions are charged and, therefore, carry a polar element that cannot diffuse through the membrane. Glucose is too large, and also contains a polar aldehyde group. Oxygen atoms generally contribute to molecular polarity due to their abundance of valence electrons. When arranged symmetrically, however, such as in the oxygen molecule, the oxygen atoms result in zero net polarity.

Transmembrane proteins and channels are used for facilitated diffusion of glucose and small ions.

The LDL-receptor enters the cell via clathrin-mediated endocytosis, not COPII. COPII is involved in budding off of the endoplasmic reticulum.

All of the other given answer options are true.

Facilitated diffusion is used to move polar or charged substances down their electrochemical gradients. Although this does require the use of integral membrane proteins, no energy is used during this process, as it is still a form of diffusion.

The direction for the diffusion of water, or osmosis, can be predicted by comparing the tonicities of the cell and its surroundings. When the cell has more solute in it than the external environment, water will flow into the cell in order to help even out the concentrations.

As a result, water will flow into the cell when it is found in a hypotonic solution.

ATP synthase is a molecule used to generate energy for the cell (in the form of ATP). Lack of ATP synthase will halt many active processes that require energy. Recall that sodium-potassium pump is found on multitude of cells in the body and functions to maintain the intracellular concentration of ions. This pump transports sodium and potassium ions against its concentration gradient (sodium out of and potassium into the cell). Since it is transporting against a concentration gradient, the sodium-potassium pump carries out active transport and, therefore, requires energy. Decreased ATP synthase activity will lead to decreased ATP levels and, subsequently, affect the sodium-potassium pump.

Potassium channels are selective molecules (selective for potassium) that transport potassium ions along its concentration gradient (from inside of cell to outside); therefore, this is a type of passive transport and does not require energy.

Membrane transporters are molecules found on plasma membranes that act as gateway for several molecules that enter and exit cells. These transporters are usually specific for one or two molecules and transport them across the cell membranes. The membrane transporters can transport ions/molecules along or against the concentration gradients; therefore, membrane transporters perform both passive and active transport. Transporters that move molecules along concentration gradient carry out a special type of passive transport called facilitated diffusion whereas transporters that move against concentration gradient carry out active transport (requires energy).

The question doesn’t state whether the molecule is brought along or against its concentration gradient; therefore, the membrane transporter could be a facilitated transporter or an active transporter.

There are two types of membrane transport: passive and active transport. Passive transport involves movement of molecules along its concentration gradient. This is a spontaneous process and does not require energy. Examples of passive transport include simple diffusion of lipophilic molecules and facilitated transport of molecules involving a membrane transporter (such as an ion channel). Active transport, on the other hand, moves molecules against their concentration gradient. This is not a spontaneous process and, therefore, requires energy.

To answer this question we need to recall the relative concentrations of the three ions presented in the question. Potassium ions are found in higher concentrations inside the cell whereas calcium and sodium are found in higher concentrations outside the cell. This means that moving calcium and sodium ions inside the cell will involve moving along their respective concentration gradients (from high to low concentration) whereas moving potassium ions inside the cell will involve moving against the concentration gradient; therefore, sodium and calcium come into the cell via passive transport whereas potassium enters via active transport.

Secondary active transport and cotransport are the same thing, and while solutes can be moved against their concentration gradient, ATP is not used. Passive and facilitated diffusion do not require ATP either. Active transport is the only transport mechanism that uses ATP to move molecules against their concentration gradient. 

Endocytosis is the process by which substances from the external environment are encapsulated in vesicles and brought into the cell. Receptor-mediated endocytosis uses membrane receptors to help localize the formation of the trasnport vesicle. Pinocytosis uses vesicles to transport fluids into the cell, while phagocytosis uses vesicles to bring pathogenic debris into the cell for digestion.

Exocytosis, in contrast, is the expulsion of substances from the cell via a transport vesicle.