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Explanation:

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Let Tm and Tb be total scores of the students majoring in Mathematics and Biology respectively.

According to the given conditions,

Tm = (M + 6) × 45

Tb = (B + 15) × 60

Also, (Tm + Tb) = (B + P + 21) × 50 

45(M + 6) + 60(B + 15) = 50M + 50B + 1050

10B – 5M + 270 + 900 = 1050

10B – 5M = –120

M = 2B + 24

Here, we need to determine the maximum value of P. 

∴ We need to minimize the value of B. Minimum value of B can be 0.

∴ M = 24

Again, we know that, 

M + B + P + 21 = 60 

⇒ 24 + 0 + P + 21 = 60

⇒ P = 15

Hence, option (d).

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