The coefficient of x¹⁰¹ in the expression (5 + x)⁵⁰⁰ + x (5 + x)⁴⁹⁹ + x²(5 + x)⁴⁹⁸ +..... + x⁵⁰⁰, x > 0, is

(A) ⁵⁰¹C₁₀₁ (5)³⁹⁹

(B) ⁵⁰¹C₁₀₁ (5)⁴⁰⁰

(C) ⁵⁰¹C₁₀₀ (5)⁴⁰⁰

(D) ⁵⁰⁰C₁₀₁ (5)³⁹⁹

Binomial Theorem and Its Simple Applications: JEE Main 2022 Mathematics question

JEE Main 2022 · 25 Jun, Evening shift · Q2937

JEE Main 202225 Jun, Evening shiftMathematicsMediumBinomial Theorem and Its Simple Applications131× since 2002

The coefficient of x¹⁰¹ in the expression

{(5 + x)^{500}} + x{(5 + x)^{499}} + {x^2}{(5 + x)^{498}} + \,\,.....\,\, + \,\,{x^{500}}

, x > 0, is

JEE Main 2022 · 25 Jun, Evening shift · Q2937

JEE Main 202225 Jun, Evening shiftMathematicsMediumBinomial Theorem and Its Simple Applications131× since 2002

The coefficient of x¹⁰¹ in the expression

{(5 + x)^{500}} + x{(5 + x)^{499}} + {x^2}{(5 + x)^{498}} + \,\,.....\,\, + \,\,{x^{500}}

, x > 0, is