Mathematics · 2014
JEE Main · 11 April 2014, Shift 1 · Q67
The coefficient of x^50 in the binomial expansion of (1+x)^1000+x(1+x)^999+x^2(1+x)^998+ ⋯ ⋯+x^1000 is:
The coefficient of $\displaystyle x^{50}$ in the binomial expansion of
$$\begin{aligned}
& (1+x)^{1000}+x(1+x)^{999}+x^2(1+x)^{998}+ \\
& \cdots \cdots+x^{1000} \text { is : }
\end{aligned}
$$
Official answer
(4)
$\displaystyle \frac{(1001)!}{(50)!(951)!}$
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JEE Main 2014 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.