nope!
Yes, "Century" should be capitalized when used in reference to a specific century, such as the 21st Century.
We are in the 21st Century.
21st century.
It is in the 21st century.
the 21st century
~this is the 21st century
Yes they do have batteries in the 21st century and had in the 20th century.
No, there is no apostrophe in the phrase "21st century."
No, the word "century" is not capitalized unless it begins a sentence. So "thirteenth century" would not be capitalized in the middle of a sentence.
characteristics of 21st century managers
is 21st century is an age of greed
The year 2010 is in the 21st century.