If D_n= vmatrix n&20&30 ^2&40&50 ^3&60&70 vmatrix then what is the value of _ n=1 ^ 4 D_n?

NDA 2024 Mathematics question

If then what is the value of ?

Answer: (A)

Only the first column depends on , so the determinants can be added column-wise: $ = =

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Question ID VK-029909