JEE Main 2022 · 30 Jul · Shift 2 · Mathematics Q66

MathematicsSingle correct+4 / -1Question 66 of 90

The coefficient of $x^{1011}$ in the expression $(1+2x)^{2022}+2x(1+2x)^{2021}+(2x)^2(1+2x)^{2020}+\dots+(2x)^{2022}$ is

{}^{2022}C_{1011}

{}^{2022}C_{1011}\times(2)^{1011}

{}^{2023}C_{1011}\times(2)^{1011}

{}^{2023}C_{1011}

Answer and worked solution

Official answer: C

Geometric sum. With ratio $\frac{2x}{1+2x}$ , the expression equals $\dfrac{(1+2x)^{2023}-(2x)^{2023}}{(1+2x)-2x}=(1+2x)^{2023}-(2x)^{2023}$ .

Coefficient ${}^{2023}C_{1011}\,2^{1011}$ .

(C)

Topics:General and middle terms Geometric progression

JEE Main 2022 · 30 Jul · Shift 2, Mathematics question 66