What are the subtle differences in meanings between the following words?
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Some of these words have multiple meanings, but I am pointing the specific meaning which is in political/social or economic context as mentioned by you. (This answer took me so much time to write, hope it helps)
Paradox (noun) means a situation or statement that seems impossible or is difficult to understand because it contains two opposite facts or characteristics.
It's a paradox that drinking too much water makes you feel thirsty.
It's a paradox that our government talks about secularism and still favours a particular religion.
Conundrum (noun) is a problem or puzzle which is difficult or impossible to solve.
We tried to empower women in the region, but they opposed us saying 'they don't want to go against their husbands.' What a conundrum!
Dilemma (noun) is a difficult situation in which you have to choose between two or more almost similarly difficult alternatives.
I was trapped between a dry well and a high end cliff, there's no place to go instead of the two. God, what a dilemma!
Our government is facing a dilemma of either being secularist or nationalist.
Plight (noun) is an unpleasant condition, especially a serious, sad, or difficult one.
My problems don't carry any significance with the plight of the storm victims.
Hope, it helped :) Oof, I am tired now.