For ~는 겁니까? and ~는 거야?, you need to know the sentence endings comprising politeness level and speech style. * Politeness level - how respectful one is to the listener. - casual: plain - for familiar people roughly your age or younger - polite: respectful - for those who are senior to you in age/position * Speech style - how rigid or smooth the speech is. - informal: smooth style - for friends, family, and anyone familiar - formal: rigid style - addressing a multitude or strangers, or writing impersonally (There are also other more obscure endings) Examples: 이다 (is/am/are - always attaches to a noun/pronoun) - interrogative form is given in []. 1) 이야/야 [이야/야?]: casual-informal. 나는 학생이야. 그 애는 학생이야? 2) 이에요/예요 [이에요/예요?]: polite-informal. 나는 학생이에요. 그 애는 학생이에요? 3) 이다 [이냐?]: casual-formal. 나는 학생이다. 그 애는 학생이냐? 4) 입니다 [입니까?]: polite-formal. 나는 학생입니다. 그 애는 학생입니까? Your first two sentences are related to #1 and #4 above. ~는 것이다 is a common sentence ending meaning "It is that ...", which is an indirection smoothing the sentence. E.g. 집안 청소를 하는 것이야 = 집안 청소를 하는 거야 (#1) = It is house cleaning I'm doing = I'm cleaning the house. And 집안 청소를 하는 것입니다 = 집안 청소를 하는 겁니다 (#4) is in a polite-formal style. Similarly, - 뭐 하는 겁니까? = 뭐 하는 것입니까?: What are you doing? (polite-formal). (무엇 = 뭐 = what, 해요 = do, is doing) - 뭐 하는 거야? = 뭐 하는 것이야?: same, in polite-formal style. * 뭐 해요? and 뭐 하는 거예요? - 뭐 해요? = 무엇을 해요?: What do you do? = What are you doing? (polite-informal) - 뭐 하는 거예요? = 무엇 하는 것이에요?: What is it you're doing? = What are you doing? (polite-informal). - 뭐 하는 겁니까?: (same) polite-formal. In these sentences, ~는 것이다 makes a minor difference, but it has a more important role in some other contexts.