In eukaryotes, sterol molecules are used to strengthen the plasma membrane. These molecules are able to pack very close together forming tight strucutres. 

In lipid bilayers, lipids molecules readily drift around laterally, they rarely flip across the membrane. Recall that the lipid bilayer can be depicted via the fluid mosaic model, as phospholipids and integral proteins are free to move laterally throughout the membrane. A flip (phospholipid from the inner leaflet to outer leaflet, or vice-versa) is thermodynamically unfavorable and does not occur as often as lateral movements. 

Chaperons are proteins that help other proteins fold properly. There are found in the interior of the cell, usually associated with ribosomes and not the cell membrane. All other functions listed are carried out by membrane proteins.

Plasma membranes are selectively permeable. Small non polar molecules like molecular oxygen and hydrocarbons can pass through the membrane while larger charged molecules like glucose cannot, unless their transport is facilitated by a membrane protein.

Only small, uncharged molecules that are nonpolar can cross the cell membrane via diffusion. For example, oxygen molecules can easily diffuse across the cell membrane. Ions like potassium and sodium can cross the cell membrane through other mechanisms, such as active transport or through ion channels, but they cannot cross via the mechanism of diffusion.

Cholesterol is a major component of the plasma membrane fluidity. If we add more of this molecule to a cell membrane in normal conditions, we would hinder the movement of other lipids and essentially cause them to be more compressed. This compression would lead to a decrease in the fluidity of the membrane.

Peripheral proteins are located either on the inside or outside of the cell, but do not pass all the way through. Glycoproteins are located on the outside of the cell membrane. Mitochondria are located within the cell and make ATP. Golgi apparatus is also located within the cell, thus does not function for transport through the membrane. Integral proteins act as carrier proteins and allow substances to pass through the cell membrane from the inside to the outside of the cell (or outside to the inside).

Active transport is when a particle moves against its concentration gradient through a selective membrane with the aid of energy. Moving down its concentration gradient and from a high to low concentration is simple diffusion. The movement of water down its concentration gradient is osmosis and moving a particle or ion through a protein is facilitated transport. These are all examples of passive transport. 

Glucose need a channel protein to pass through the membrane because it is too large. Substances that pass through the membrane via simple diffusion need to be relatively small and not charged. Carbon dioxide and oxygen gas are both small nonpolar molecules that can easily diffuse through the plasma membrane. 

Only two choices are correct, facilitative diffusion and active transport because they both need carrier proteins for transport across the cell membrane. Simple diffusion does not require carrier proteins.