If P=n(n^2-1^2)(n^2-2^2)(n^2-3^2) (n^2-r^2), n>r, n N , then P is divisible by

JEE Advanced Mathematics question

If , , , then is divisible by

Answer: (B),(C)

Factorise each :

P=n(n-1)(n+1)(n-2)(n+2)·s(n-r)(n+r)=(n-r)(n-r+1)·s(n-1) n (n+1)·s(n+r),

a product of consecutive integers. The product of any consecutive integers is divisible by (since

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Question ID VK-108234