Read the following passage and solve the questions based on it.
Each group of questions in this section is based on a set of conditions. While answering some of the questions, it may be useful to draw a rough diagram. Choose the response that most accurately and completely answers each question.
Seven instructors—J, K, L, M, N, P and Q, teach management courses at a premier institute in east India. Each instructor teaches during only one term; either the first term, or the second term, or the third term. The following conditions apply:
(i) K teaches during the third term.
(ii) L and M teach during the same term.
(iii) Q teaches during either the first term or the second term.
(iv) Exactly twice as many instructors teach during the third term as compared to the first term.
(v) N and Q teach during different terms.
(vi) J and P teach during different terms.
Which one of the following cannot be true?