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Question

If $$n$$ is a whole number greater than 1, then $$n^{2} (n^{2} - 1)$$ is always divisible by:


A
12
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B
12 and 24
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C
24
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D
36
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Solution

The correct option is A $$12$$
If n is whole number greater than 1 then the least value of n will be
$$n=2,3,4,5.......$$
Now given that $$n^2(n^2-1)$$
$$n^2(n+1)(n-1)$$..........($$a^2-b^2=(a+b)(a-b)$$)
least value for n =2. now put it given expression 
$$2^2(2+1)(2-1)$$
$$4\times 3\times 1=12$$
hence the expression always will be divisible by $$12$$
hence option $$A$$ is correct.

Mathematics

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