Necrosis is due to lack of oxygen and nutrients to the cell, which leads to its death. On the other hand, apoptosis is referring to cell suicide. It is getting enough oxygen and nutrients but it has lived as long as it can live.
There is no inflammation associated with apoptosis.
Necrosis is a word that describes the morphological changes that occur to a cell after its death. These include the following: (1) cellular swelling (2) denaturation of cytoplasmic proteins (gives rise to eosinophilia) (3) breakdown of cell organelles (4) a sequence of nuclear changes which include (a) karyolysis (b) pyknosis (c) karyorrhexis. There is inflammation.
How do remember this? pyknosis is the first thing that happens and is characterized by nuclear shrinkage (the word "pyknosis" reminds me of my pinky finger, the smallest finger, and so that is how I remember that pyknosis referst to nuclear shrinkage). Karyolysis refers to nuclear swelling not breakup because that is the karyorrhexis part of it. T. Rex, the dinasour, is going to breakup the nuclear membrane. Simply these three words are associated with breakdown of the nucleus.
Now try to answer the question.