Question

How much did Dipan get in English Paper II?

• A. 94
• B. 96.5
• C. 97
• D. 98
• E. 99
• A. 1
• B. 2
• C. 3
• D. 4
• J. 5
• A. Pritam, Joseph, Tirna, Agni
• B. Joseph, Tirna, Agni, Pritam
• C. Pritam, Agni, Tirna, Joseph
• D. Joseph, Tirna, Pritam, Agni
• O. Pritam, Tirna, Agni, Joseph
• A. Shreya
• B. Ram
• C. Ayesha
• D. Dipan
• T. No one from the top ten
• A. Ram
• B. Agni
• C. Pritam
• D. Ayesha
• Y. Dipan

Answer 1

The Correct Option is C

From the table, Dipan’s Final Score is \(96.0\). The Final Score is the average of five Group Scores: PCB, Mathematics, Social Science, Vernacular, and English.
Dipan’s Group Scores:
- PCB: \((98 + 98 + 98)/3 = 98\)
- Mathematics: 95
- Social Science: \((96 + 95)/2 = 95.5\)
- Vernacular: \((96 + 94)/2 = 95\)
- English: \((96 + x)/2\), where \(x\) is English Paper II.
Final Score equation: \[ \frac{98 + 95 + 95.5 + 95 + \frac{96 + x}{2}}{5} = 96 \] \[ \Rightarrow 383.5 + \frac{96 + x}{2} = 480 \] \[ \frac{96 + x}{2} = 96.5 \quad \Rightarrow \quad 96 + x = 193 \quad \Rightarrow \quad x = 97 \] Thus, English Paper II score is \( \boxed{97} \).

Answer 2

Ram: Yes.
- Ram's marks are compared to the required threshold of ≥95 in each subject:

• PCB: Ram scored ≥95 in Physics, Chemistry, and Biology.
• Math: Ram scored ≥95 in Mathematics.
• Soc. Sci: Ram scored ≥95 in Social Science.
• Vernacular: Ram scored ≥95 in Vernacular.
• English: Ram scored ≥95 in English.

Since all the subject marks are ≥95, Ram satisfies the condition.

Dipan: Yes. 
- Dipan's marks are also compared to the required threshold of ≥95 in each subject:

• PCB: Dipan scored ≥95 in Physics, Chemistry, and Biology.
• Math: Dipan scored ≥95 in Mathematics.
• Soc. Sci: Dipan scored ≥95 in Social Science.
• Vernacular: Dipan scored ≥95 in Vernacular.
• English: Dipan scored ≥95 in English.

Since all the subject marks are ≥95, Dipan satisfies the condition.

Sagnik: Yes. 
- Sagnik's marks are compared to the required threshold of ≥95 in each subject:

• PCB: Sagnik scored ≥95 in Physics, Chemistry, and Biology.
• Math: Sagnik scored ≥95 in Mathematics.
• Soc. Sci: Sagnik scored ≥95 in Social Science.
• Vernacular: Sagnik scored ≥95 in Vernacular.
• English: Sagnik scored ≥95 in English.

Since all the subject marks are ≥95, Sagnik satisfies the condition.

Sanjiv: No. 
- Sanjiv's marks are compared to the required threshold of ≥95 in each subject:

• PCB: Sanjiv scored ≥95 in Physics, Chemistry, and Biology.
• Math: Sanjiv scored ≥95 in Mathematics.
• Soc. Sci: Sanjiv scored ≥95 in Social Science.
• Vernacular: Sanjiv's Vernacular Paper II score is <95, which fails the requirement for Vernacular.
• English: Sanjiv scored ≥95 in English.

Since Sanjiv's Vernacular Paper II score is <95, Sanjiv does not satisfy the condition.

Joseph: No. 
- Joseph's marks are compared to the required threshold of ≥95 in each subject:

• PCB: Joseph scored <95 in Physics, Chemistry, and Biology.
• Math: Joseph scored ≥95 in Mathematics.
• Soc. Sci: Joseph scored ≥95 in Social Science.
• Vernacular: Joseph scored ≥95 in Vernacular.
• English: Joseph scored ≥95 in English.

Since Joseph's PCB score is <95, Joseph does not satisfy the condition.

Agni: No. 
- Agni's marks are compared to the required threshold of ≥95 in each subject:

• PCB: Agni scored ≥95 in Physics, Chemistry, and Biology.
• Math: Agni scored ≥95 in Mathematics.
• Soc. Sci: Agni scored ≥95 in Social Science.
• Vernacular: Agni's Vernacular Paper I score is <95, which fails the requirement for Vernacular.
• English: Agni scored ≥95 in English.

Since Agni's Vernacular Paper I score is <95, Agni does not satisfy the condition.

Pritam: No. 
- Pritam's marks are compared to the required threshold of ≥95 in each subject:

• PCB: Pritam scored ≥95 in Physics, Chemistry, and Biology.
• Math: Pritam scored ≥95 in Mathematics.
• Soc. Sci: Pritam's Social Science Paper I score is <95, which fails the requirement for Social Science.
• Vernacular: Pritam scored ≥95 in Vernacular.
• English: Pritam scored ≥95 in English.

Since Pritam's Social Science Paper I score is <95, Pritam does not satisfy the condition.

Conclusion: Exactly 3 boys (Ram, Dipan, and Sagnik) satisfy the condition of having ≥95 in all relevant subjects.

Answer 3

Recalculate final scores for each after replacing Social Science Group score with 100:
- Pritam: New average rises significantly (biggest improvement).
- Joseph: Next highest improvement.
- Tirna: Slightly less improvement than Joseph.
- Agni: Least improvement among the four.
Thus, the order is \( \boxed{\text{Pritam, Joseph, Tirna, Agni}} \).

Answer 4

Eligibility requires ≥95 in every group score. Checking: Ram meets the condition and has highest Social Science Group score among eligible students. Thus, prize goes to \( \boxed{\text{Ram}} \).

Answer 5

Improving one paper to 100 gives maximum benefit to the student with the largest gap between their lowest paper score and 100, especially if that paper belongs to a group with a low average. Pritam benefits the most, overtaking all others in final score.