Pain is suffering or hurt, so choice d is the essential element. Without hurt, there is no pain. A cut (choice a) or a burn (choice b) may cause pain, but so do many other types of injury. A nuisance (choice c) is an annoyance that may or may not cause pain.

The essential part of a monopoly is that it
involves exclusive ownership or control.

A gala indicates a celebration, the necessary element here. A tuxedo (choice b) is not required garb at a gala, nor is an appetizer (choice c). A gala may be held without the benefit of anyone speaking (choice d).

Lightning is produced from a discharge of electricity, so electricity is essential. Thunder and rain are not essential to the production of lightning (choices b and d). Brightness may be a byproduct of lightning, but it is not essential (choice c).

To harvest something, one must have a crop,
which is the essential element for this item. Autumn (choice a) is not the only time crops are harvested. There may not be enough of a crop to stockpile (choice b), and you can harvest crops without a tractor (choice c).

A dimension is a measure of spatial content. A compass (choice a) and ruler (choice b) may help determine the dimension, but other instruments may also be used, so these are not the essential element here. An inch (choice c) is
only one way to determine a dimension.

An antique is something that belongs to, or
was made in, an earlier period. It may or may not be a rarity (choice a), and it does not have to be an artifact, an object produced or shaped by human craft (choice b). An antique is old but does not have to be prehistoric (choice d).

Knowledge is understanding gained through
experience or study, so learning is the essential element. A school (choice a) is not necessary for learning or knowledge to take place, nor is a teacher or a textbook (choices b and c).

An itinerary is a proposed route of a journey. A map (choice a) is not necessary to have a planned route. Travel (choice c) is usually the outcome of an itinerary, but not always. A guidebook (choice d) may be used to plan the journey but is not essential.

An orchestra is a large group of musicians, so musicians are essential. Although many orchestras have violin sections, violins aren't essential to an orchestra (choice a). Neither a stage (choice b) nor a soloist (choice d) is necessary.