MathsJEE Main 23 Jan 2026, Shift 1·Q12·MCQ·Moderate

Binomial Theorem · Sum of binomial coefficients

The value of

\dfrac{{}^{100}C_{50}}{51} + \dfrac{{}^{100}C_{51}}{52} + \ldots + \dfrac{{}^{100}C_{100}}{101}

is:

(1) $\dfrac{2^{101}}{100}$
(2) $\dfrac{2^{100}}{100}$
(3) $\dfrac{2^{101}}{101}$
(4) $\dfrac{2^{100}}{101}$

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