Analyzing Student Enrollment and Vacant Seats

This question asks us to find the course that had the minimum number of total vacant seats over a five-year period, from 2016 to 2020. We are given a table showing the enrollment figures for five different courses in these years, along with the maximum seat capacity for each course.

The courses and their maximum seat capacities are:

• BTech: 60 seats
• MCA: 60 seats
• MTech: 30 seats
• MPhil: 20 seats
• Integrated MTech: 30 seats

Understanding Vacant Seats

Vacant seats for a course in a specific year can be calculated by subtracting the number of enrolled students from the maximum number of seats available for that course in that year.

Formula for Vacant Seats:

Vacant Seats = Maximum Seats $-$ Enrolled Students

Calculating Total Vacant Seats per Course (2016-2020)

To find the course with the minimum total vacant seats, we need to calculate the total vacant seats for each of the five courses across the five years (2016 to 2020). This involves calculating the vacant seats for each course in each year and then summing up these yearly vacant seats for each course.

1. BTech Course Vacant Seats

Maximum Seats for BTech = 60

• 2016: \(60 - 45 = 15\)
• 2017: \(60 - 55 = 5\)
• 2018: \(60 - 48 = 12\)
• 2019: \(60 - 53 = 7\)
• 2020: \(60 - 50 = 10\)

Total Vacant Seats for BTech = \(15 + 5 + 12 + 7 + 10 = 49\)

2. MCA Course Vacant Seats

Maximum Seats for MCA = 60

• 2016: \(60 - 52 = 8\)
• 2017: \(60 - 56 = 4\)
• 2018: \(60 - 43 = 17\)
• 2019: \(60 - 40 = 20\)
• 2020: \(60 - 46 = 14\)

Total Vacant Seats for MCA = \(8 + 4 + 17 + 20 + 14 = 63\)

3. MTech Course Vacant Seats

Maximum Seats for MTech = 30

• 2016: \(30 - 25 = 5\)
• 2017: \(30 - 26 = 4\)
• 2018: \(30 - 21 = 9\)
• 2019: \(30 - 23 = 7\)
• 2020: \(30 - 28 = 2\)

Total Vacant Seats for MTech = \(5 + 4 + 9 + 7 + 2 = 27\)

4. MPhil Course Vacant Seats

Maximum Seats for MPhil = 20

• 2016: \(20 - 16 = 4\)
• 2017: \(20 - 18 = 2\)
• 2018: \(20 - 14 = 6\)
• 2019: \(20 - 15 = 5\)
• 2020: \(20 - 13 = 7\)

Total Vacant Seats for MPhil = \(4 + 2 + 6 + 5 + 7 = 24\)

5. Integrated MTech Course Vacant Seats

Maximum Seats for Integrated MTech = 30

• 2016: \(30 - 26 = 4\)
• 2017: \(30 - 24 = 6\)
• 2018: \(30 - 25 = 5\)
• 2019: \(30 - 23 = 7\)
• 2020: \(30 - 27 = 3\)

Total Vacant Seats for Integrated MTech = \(4 + 6 + 5 + 7 + 3 = 25\)

Comparing Total Vacant Seats

Now let's list the total vacant seats calculated for each course from 2016 to 2020:

Comparing these totals, we can see the following:

• BTech: 49
• MCA: 63
• MTech: 27
• MPhil: 24
• Integrated MTech: 25

The minimum number among these totals is 24.

Identifying the Course with Minimum Vacant Seats

The course with the minimum number of total vacant seats during the period 2016 to 2020 is MPhil, with a total of 24 vacant seats.

Revision Table: Key Calculations

Comparing the 'Total Vacant Seats (2016-2020)' column confirms that MPhil has the minimum total vacant seats (24).

Additional Information: Data Analysis Tips

Analyzing data presented in tables, especially in competitive exams, often requires careful calculation and comparison. Here are a few tips:

• Read the Question Carefully: Understand exactly what is being asked (e.g., total over a period, minimum/maximum value, specific year).
• Identify Relevant Data: Locate the numbers in the table needed for your calculation. Pay attention to notes or brackets (like the maximum seats here).
• Break Down Calculations: For problems spanning multiple years or categories, calculate intermediate values (like yearly vacant seats) before summing them up.
• Organize Your Work: Using a table or list for intermediate results, as done above, can help prevent errors and makes comparison easier.
• Double-Check Calculations: Simple arithmetic errors are common. Quickly reviewing your sums can save you from choosing the wrong answer.
• Compare Clearly: Once you have the final totals, list them out explicitly to make the comparison for minimum or maximum values straightforward.

Understanding concepts like 'vacant seats' based on 'maximum capacity' and 'enrollment' is key to solving such data interpretation problems.