The greatest coefficient in the expansion of (1+x)^{2n+2} is

A)\((2n)!\over(n!)^2\)

B)\((2n+2)!\over[(n+1)!]^2\)

C)\((2n+2)!\over n!(n+1)!\)

D) \((2n)!\over n!(n+1)!\)

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correct option is B) \((2n+2)!\over [(n+1)!]^2\)

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