Learn English – word that means nonsensical question

A friend of mine and I were joking about questions that are complete nonsense. Here are some examples:

True or false: How tall is the Empire State Building?

Is it further to Pittsburgh or by train?

How tall do you weigh?

I called them nonsensical questions. My friend said he thought there was a more descriptive word for them, but could not remember the word. Is there a word for questions that are complete nonsense? I am dubious of his claim.

Edit: I just suggested the word balderdash, but he said that is not the word he was trying to remember. He says he is thinking of a word that specifically implies a question is nonsense. It would not be used to describe other types of sentences, like statements.

Edit 2: Someone requested that I add the following question: "Which weighs more, a pound of bricks or a pound of feathers?" This question is a trick question, but not nonsensical. A similar question that is closer to being nonsensical would be

Which weighs more, a pound of gold or a pound of feathers?

Comparing the weight of gold to the weight of feathers is ambiguous. Both bricks and feathers are typically weighed using the standard scale. Gold, on the other hand, is typically weighed using the Troy scale. A troy pound weighs less than a standard avoirdupois pound. So, the question does not have as straightforward an answer due to the ambiguity of which scale is being used to weigh each.