The sum of the coefficients of x⁴⁹⁹ and x⁵⁰⁰ in (1+x)¹⁰⁰⁰+x(1+x)⁹… | JEE Main 2026 Mathematics PYQ | Jeeify

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MCQMediumJEE Main 2026 · 28 January, Shift 2Simple Applications

The sum of the coefficients of $x^{499}$ and $x^{500}$ in $(1+x)^{1000}+x(1+x)^{999}+x^2(1+x)^{998}+\cdots+x^{1000}$ is:

A
${}^{1000}C_{501}$
B
${}^{1002}C_{500}$
C
${}^{1001}C_{501}$
D
${}^{1002}C_{501}$

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