Examine the information given in the following paragraph and answer the items that follow: Guest lectures on five subjects viz., Economics, History, Statistics, English and Mathematics have to be arranged in a week from Monday to Friday. Only one lecture can be arranged on each day. Economics cannot be scheduled on Tuesday. Guest faculty for History is available only on Tuesday. Mathematics lecture has to be scheduled immediately after the day of Economics lecture. English lecture has to be scheduled immediately before the day of Economics lecture. Which lecture is the last one in the week?

The problem requires scheduling five lectures (Economics, History, Statistics, English, Mathematics) from Monday to Friday, with one lecture per day.

Let's break down the constraints:

1. History lecture is only available on Tuesday. This fixes History on Tuesday. Schedule so far: Monday: Tuesday: History Wednesday: Thursday: Friday:

2. English lecture has to be scheduled immediately before Economics, and Mathematics lecture has to be scheduled immediately after Economics. This forms a block of three consecutive lectures: English -> Economics -> Mathematics (En-E-M).

3. Economics cannot be scheduled on Tuesday.

Now, let's place the En-E-M block. This block requires three consecutive days. Given History is on Tuesday, the only remaining block of three consecutive days is Wednesday-Thursday-Friday. If we place En-E-M in Wednesday-Thursday-Friday: Wednesday: English Thursday: Economics Friday: Mathematics

Let's check if this satisfies all conditions:

• History on Tuesday: Yes.
• English before Economics, Mathematics after Economics: Yes (Wed-Thu-Fri).
• Economics not on Tuesday: Yes (Economics is on Thursday).

This schedule works. The remaining subject is Statistics, which must be on Monday. Final Schedule: Monday: Statistics Tuesday: History Wednesday: English Thursday: Economics Friday: Mathematics

The question asks which lecture is the last one in the week. Based on the schedule, the lecture on Friday is Mathematics.

Therefore, Mathematics is the last lecture in the week.

The final answer is C) Mathematics.