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JEE Advanced Mathematics question

MathematicsDeterminantsJEE Advanced

Let

f(n)=,

where the symbols have their usual meanings. The is divisible by

Answer: (A),(C)

Solution

Use and :

f(n)=.

Apply , then . Use and :

f(n)=Missing \end{vmatrix}\begin{vmatrix} n & 1 & 1 n! & n· n! & (n+1)(n+1)!

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Question ID VK-108290