What is the relevance of North Karnataka towards the economy of Karnataka as a state?

 North Karnataka was actually less productive region in Karnataka because it was ruled by Persian and Urdu rulers who concentrated less on the region's development another reason being it is one of the driest places in India and an arid and semi-arid landscape.

However nowadays - Gulbarga, Raichur, Hubballi Dharwad, Bagalkote, Bijapura, Bidar are moderately developed decent cities and are actually less polluted compared to Delhi, Hyderabad, Mumbai, Kolkata , Noida and other big cities.

Gulbarga is the largest city and economic capital of North Karnataka.

Raichur is known for Hatti Gold Fields inspite of Telugu population.

Gulbarga, Bijapura, Bagalkote and Hubballi also contribute atleast a small percentage towards economy of Karnataka state.

However Mandya is the largest city in Karnataka and the most developed city in Karnataka followed by Hassan and Davangere and Gulbarga.

What is the most useless country in the world in terms of resources, economy, etc.?

 Most likely Tuvalu.

Tuvalu is an island nation in the South Pacific and midway between Hawaii and Australia in the Polynesian part of Oceania.

The entire country is 25 square kilometers with about 10000 people and the only occupation you can do in Tuvalu is fishing. Sadly for Tuvalu, tourism is not big here and it doesn’t have hotels and it is one of the least visited countries in the world.

The country has no water resources and nor does it have rivers or soil to cultivate anything so pretty much everything has to be imported.

Surprisingly, this country has a per capita GDP of over $6000 pp on nominal basis so I guess they must catch a lot of fish and they also generate revenue by issuing fishing licenses.

Essentially, Tuvalu is just a strip of land in the middle of the ocean with nothing in terms of natural resources except the ocean sorrounding it.

I don’t know if it’s a useless country but the entire country’s GDP is $63 million, probably less than what a single Costco generates in revenue in a year.

Rising sea levels also pose grave danger to this country and just like Maldives and Kiribati, Tuvalu is at risk of becoming the next Atlantis.