The first year students in a business school are split into six sections. In 2019 the Business Statistics course was taught in these six sections by Annie, Beti, Chetan, Dave, Esha, and Fakir. All six sections had a common midterm (MT) and a common endterm (ET) worth 100 marks each. ET contained more questions than MT. Questions for MT and ET were prepared collectively by the six faculty members. Considering MT and ET together, each faculty member prepared the same number of questions. 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.

The following additional facts are known.

i. Annie prepared the fifth question for both MT and ET. For MT, this question carried 5 marks.

ii. Annie prepared one question for MT. Every other faculty member prepared more than one questions for MT.

iii. All questions prepared by a faculty member appeared consecutively in MT as well as ET.

iv. Chetan prepared the third question in both MT and ET; and Esha prepared the eighth question in both.

v. Fakir prepared the first question of MT and the last one in ET. Dave prepared the last question of MT and the first one in ET.

The second question in ET was prepared by:

Let us analyze the constraints given for Midterm (MT) and Endterm (ET):

MT has at least 4 questions of 5 marks, at least 3 of 10 marks, and at least 2 of 15 marks. The minimum total marks for MT is:
$4\times 5+3\times 10+2\times 15=20+30+30=80$ marks.

Since the total marks must be exactly 100, we can add more questions to reach 100 marks. Similarly, ET also totals 100 marks. Let the number of 5, 10, and 15-mark questions in MT be $n_5,n_{10},n_{15}$ respectively, and in ET be $m_5,m_{10},m_{15}$.

Given ET has more questions than MT. Let us evaluate the possibilities for MT.
If MT has 4 questions of 5 marks, 5 questions of 10 marks, and 2 questions of 15 marks: $20+50+30=100$ marks (Total 11 questions).
If MT has 6 questions of 5 marks, 4 questions of 10 marks, and 2 questions of 15 marks: $30+40+30=100$ (Total 12 questions). But from (i), Annie's 5th question in MT has 5 marks, which means there must be at least 5 questions of 5 marks in MT.

Let's map out the positions in ET. Dave prepared the first question in ET (from fact v). Since all questions by any faculty member must be consecutive (fact iii), and Dave prepared more than one question in MT, let's analyze ET. Dave prepared the first question. If Dave prepares multiple questions, they must start at position 1. Since Chetan prepares the 3rd question in ET, Dave can prepare at most 2 questions in ET (positions 1 and 2). Since Dave prepares at least two questions in ET, Dave must prepare exactly the 1st and 2nd questions in ET. Therefore, the second question in ET is prepared by Dave.