To determine the year in which the ratio of admitted students in the B.A. program to those in all the programs is the lowest, we need to calculate the ratio for each year and compare them.

Step 1: Calculate Total Students for Each Year

• For 2021: Total students = 150 (B.A.) + 25 (B.Sc.) + 50 (B.B.A.) + 45 (B.Com.) + 75 (B.C.A) = 345
• For 2022: Total students = 225 + 40 + 45 + 62 + 70 = 442
• For 2023: Total students = 450 + 65 + 30 + 90 + 73 = 708
• For 2024: Total students = 470 + 73 + 35 + 105 + 70 = 753
• For 2025: Total students = 500 + 80 + 36 + 132 + 74 = 822

Step 2: Compute the Ratio of B.A. Students to Total Students for Each Year

• For 2021: Ratio = \(\frac{150}{345}\)
• For 2022: Ratio = \(\frac{225}{442}\)
• For 2023: Ratio = \(\frac{450}{708}\)
• For 2024: Ratio = \(\frac{470}{753}\)
• For 2025: Ratio = \(\frac{500}{822}\)

Step 3: Calculate the Numerical Value of Each Ratio

• 2021: \(\frac{150}{345} \approx 0.4348\)
• 2022: \(\frac{225}{442} \approx 0.5090\)
• 2023: \(\frac{450}{708} \approx 0.6356\)
• 2024: \(\frac{470}{753} \approx 0.6245\)
• 2025: \(\frac{500}{822} \approx 0.6083\)

Conclusion: The lowest ratio of B.A. students to total students occurs in the year 2021, with a ratio of approximately 0.4348.