If 'COMPUTER' is decoded as '3,15,13,16,21,20,5,18'. Then 'MATHEMATICS' is decoded as:
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13,1,20,8,5,1,31,20,9,3,1,9
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13,1,20,8,5,13,1,20,9,3,19
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1,3,1,20,8,5,1,3,2,9,13,19
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13,1,20,8,15,13,20,9,13,19
The coding pattern converts each letter to its position in the alphabet: C=3, O=15, M=13, P=16, U=21, T=20, E=5, R=18. Applying this to MATHEMATICS: M=13, A=1, T=20, H=8, E=5, M=13, A=1, T=20, I=9, C=3, S=19. Option A incorrectly includes 31 and has the wrong sequence, while option C and D have incorrect letter positions.
Here each letter is simply replaced by its position in the alphabet (A=1, B=2, ... Z=26), so COMPUTER becomes 3,15,13,16,21,20,5,18 exactly as given. Applying the same rule to MATHEMATICS (M=13, A=1, T=20, H=8, E=5, M=13, A=1, T=20, I=9, C=3, S=19) gives 13,1,20,8,5,13,1,20,9,3,19.