Example sentences
wǒ我yǒu有yí一gè个wèn问tí题。
I have a question.
zhè这ge个wèn问tí题hěn很nán难huí回dá答。
This question is hard to answer.
About this word
问 is to ask, 题 is a topic or a subject for discussion, so 问题 is the thing you raise. That one image covers both English senses, the question you pose and the problem you have. 我问你一个问题 is a question. 这个问题很难 could be either. 没问题 is the standard way to say no problem or sure. 问 alone is a verb, so you cannot say 一个问; the syllable needs 题 before it can be a noun.
The story behind the character
问
问 is 口 (mouth) under 门, and 门 is there only for the sound. Xu Shen wrote 问，讯也: to ask is to interrogate, to go pry the answer loose. So the character is just a mouth, which is honest enough. A 问题 is what comes out of it when you don't know and want to.
题
题 is 是 giving the sound with 页 on the right. 页 is a head. Xu Shen defined 题 as 頟也, the forehead, the front of the skull. From "front of the head" it slid into "the heading of a text," and then into 问题, a question, the front edge of something you don't know yet.