The definite article the is used before a proper noun when it is qualified by an adjective.
example
The immortal Shakespeare.
The great Caesar.
But in the following sentence
I think the should be used before populous and politically important because populous and politically important are adjective and Uttar pradesh is a proper noun.
I found the explanation in COLLINS COBUILD ENGLISH GUIDES 3: ARTICLES by Roger Berry
The short answer is - No, you shouldn't place an article before Uttar pradesh, because it's an administrative region of a country.
In 7.3 Geographical and place names without an article, p57:
Political and administrative regions of countries, for example:
California, Hampshire.
...in a little valley of Bavaria.
...at his home in Kent.
In your question, Uttar Pradesh is a state in northern India, so it is not preceded by an article.
However, the 2 examples in your question have "the" before names(proper nouns). This is just stressing, as explained below:
In 7.13 Personal names, p63:
You can stress the definite article with names of people to mean someone famous: 'I met Paul McCartney the other day.' 'You mean the Paul McCartney?'
A more general usage is also described in 4.14 Stressed 'the' meaning 'best', p34:
People sometimes stress the definite article to indicate that something is the best, most fashionable, or only thing of a particular kind. For example, someone might say 'It's the place to go' (with the pronounced /ði:/) when referring to a discotheque or club which is very good or fashionable.
Billiards is the game.
The foregoing scenario in no way pretends to present the answer to urban transportation problems.
In that book, I didn't find examples that has an adjective right before the proper noun. But I think it probably doesn't matter. Otherwise the book should have noted.
