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Explanation:

Each of MT and ET had at least four questions that were worth 5 marks, at least three questions that were worth 10 marks, and at least two questions that were worth 15 marks. In both MT and ET, all the 5-mark questions preceded the 10-mark questions, and all the 15-mark questions followed the 10-mark questions.

Therefore, Each of MT and ET had at least 4 + 3 + 2 = 9 questions. Also, these 9 questions were worth 80 marks. So, remaining 20 marks can be from (one 5-mark and one 15-mark questions OR two 10-mark questions OR two 5-mark questions and one 10-mark question OR four 5-mark questions).

From (ii), Annie prepared exactly one question (i.e., fifth question) for MT and minimum number of questions in MT = 1 + 5 × 5 = 11

From (iv) and (v), Fakir and Chetan prepared the first and the third questions respectively. Now from (ii) and (iii), Fakir and Chetan prepared the second and the fourth questions also.
 
Similarly it can be concluded that Dave prepared first two questions of ET and Chetan prepared the third and the fourth questions of ET.
 
Also, as each faculty member prepared the same number of questions and Chetan prepared 4 questions, each prepared 4 questions.
 
Total number of questions in ET and MT together = 4 × 6 = 24. As ET contained more questions than MT, MT had 11 questions and ET had 13 questions.
 
Therefore, Beti (6th and 7th), Esha (8th and 9th) and Dave (10th and 11th) prepared exactly two questions for MT. Also, first five questions were of 5 marks, then three 10-mark questions and in the last, three 15- mark questions. As ET has 13 questions and 9 among these contribute to 80 marks, we are left with the possibility that there were four 5-mark questions other than the 9 questions.
 
Annie prepared 3 questions for ET (i.e.,  the 5th, 6th and 7th). Esha prepared 8th and 9th questions. And Fakir prepared last two questions. Thus, we have

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There were eight 5-mark questions in ET and five 5-mark questions in MT.

Thus, there were 13 (5-mark) questions in MT and ET combined.

Hence, option (a).

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