MathsJEE Main 28 Jan 2026, Shift 2·Q2·MCQ·Moderate

Binomial Theorem · Sum of binomial coefficients

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

(1) ${}^{1001}C_{501}$
(2) ${}^{1002}C_{500}$
(3) ${}^{1002}C_{501}$
(4) ${}^{1000}C_{501}$

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