The coefficient of x^n in the polynomial (x+ ^nC_0 ) (x+3 , ^nC_1 ) (x+5 , ^nC_2 ) [x+(2n+1) , ^nC_n ]

JEE Main Mathematics question

The coefficient of in the polynomial \left(x+{}^nC_0\right)\left(x+3\,{}^nC_1\right)\left(x+5\,{}^nC_2\right)\ldots\left[x+(2n+1)\,{}^nC_n\right]

Answer: (C)

The product has linear factors, so the coefficient of is the sum of the constant terms,

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Question ID VK-021053