Analyzing Student Enrollment Data and Vacant Seats

The question asks us to identify the year with the highest number of vacant seats based on the provided table showing student enrollment across five different courses over five years. The table also specifies the maximum number of seats available for each course.

Understanding Vacant Seats Calculation

To find the number of vacant seats for a particular course in a specific year, we need to subtract the number of enrolled students from the maximum number of seats available for that course. The formula is:

Vacant Seats = Maximum Seats - Enrolled Students

The maximum number of seats for each course is given in the table's column headers in parentheses:

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

Calculating Total Vacant Seats for Each Year

To find the total number of vacant seats in a given year, we sum the vacant seats for all five courses in that year. Let's calculate the vacant seats for each year:

Year 2016:

• BTech: \(60 - 45 = 15\)
• MCA: \(60 - 52 = 8\)
• MTech: \(30 - 25 = 5\)
• Mphil: \(20 - 16 = 4\)
• Integrated MTech: \(30 - 26 = 4\)

Total vacant seats in 2016 = \(15 + 8 + 5 + 4 + 4 = 36\)

Year 2017:

• BTech: \(60 - 55 = 5\)
• MCA: \(60 - 56 = 4\)
• MTech: \(30 - 26 = 4\)
• Mphil: \(20 - 18 = 2\)
• Integrated MTech: \(30 - 24 = 6\)

Total vacant seats in 2017 = \(5 + 4 + 4 + 2 + 6 = 21\)

Year 2018:

• BTech: \(60 - 48 = 12\)
• MCA: \(60 - 43 = 17\)
• MTech: \(30 - 21 = 9\)
• Mphil: \(20 - 14 = 6\)
• Integrated MTech: \(30 - 25 = 5\)

Total vacant seats in 2018 = \(12 + 17 + 9 + 6 + 5 = 49\)

Year 2019:

• BTech: \(60 - 53 = 7\)
• MCA: \(60 - 40 = 20\)
• MTech: \(30 - 23 = 7\)
• Mphil: \(20 - 15 = 5\)
• Integrated MTech: \(30 - 23 = 7\)

Total vacant seats in 2019 = \(7 + 20 + 7 + 5 + 7 = 46\)

Year 2020:

• BTech: \(60 - 50 = 10\)
• MCA: \(60 - 46 = 14\)
• MTech: \(30 - 28 = 2\)
• Mphil: \(20 - 13 = 7\)
• Integrated MTech: \(30 - 27 = 3\)

Total vacant seats in 2020 = \(10 + 14 + 2 + 7 + 3 = 36\)

Comparing Total Vacant Seats by Year

Now, let's list the total vacant seats calculated for each year:

• 2016: 36
• 2017: 21
• 2018: 49
• 2019: 46
• 2020: 36

Comparing these totals, we can see that the highest number of vacant seats is 49, which occurred in the year 2018.

Conclusion: Identifying the Year with Most Vacant Seats

Based on the calculations, the year 2018 had the highest number of vacant seats among the five years presented in the table.

Revision Table: Summary of Vacant Seats Calculation

Additional Information: Interpreting Enrollment and Vacant Seat Data

Understanding vacant seats is important for educational institutions. A high number of vacant seats in a particular course or year could indicate lower demand, issues with the course offering, or perhaps external factors affecting student applications. Conversely, low vacant seats mean high demand. Analyzing trends over several years helps in planning and resource allocation. For instance, while 2018 had the highest overall vacant seats, the MCA course consistently showed a notable number of vacant seats in several years (17 in 2018, 20 in 2019), which might warrant further investigation into student interest or capacity.