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Professor Bhatnagar works only on Sundays, Mondays, Tuesdays, Thursdays and Fridays. She performs four different activities- lecturing, conducting quizzes, evaluating quizzes and working on consultancy projects. Each working day she performs exactly one activity in the morning and exactly one activity in the afternoon. During each week her work Schedule $MUST$ satisfy the following restrictions.

She conducts quizzes on exactly three mornings. If she conducts quizzes on Sunday, she does not conduct a quiz on Monday. She lectures in the afternoon on exactly two consecutive calendar days. She evaluates quizzes on exactly one morning and three afternoons. She works on consultancy project on exactly one morning. On Friday, she neither lectures nor conducts quizzes.

Which one of the following statements must be $true$ ?

1. She works on consultancy project on one of the days on which she evaluates quizzes.
2. There is one day on which she evaluates quizzes both in the morning and in the afternoon.
3. She lectures on one of the days on which she conducts quiz.
4. She lectures on one of the days on which evaluates quizzes.

Option C. She lectures on one of the days on which she conducts quiz.

From the given conditions She can conducts quiz on  $\left.\begin{matrix} Sunday & Tuesday & Thursday\\ Monday & Tuesday & Thursday \end{matrix}\right\} or$

and she can lectures on $\left.\begin{matrix} Sunday & Monday\\ Monday & Tuesday \end{matrix}\right\} or$

So, there will be definitely one on which she lectures and conducts quiz.

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1. She lectures on one of the days on which evaluates quizzes.
20 points