JEE Main 2022 · MathsMultiple choiceSingle correctMediumApplication

JEE Main 30 July 2022, Shift 2, Maths Q66

Question 66 of 90 in this shift, Maths question 6 of 30, Section A.

The coefficient of

x^{1011}

in the expression

(1+2x)^{2022} + 2x\,(1+2x)^{2021} + (2x)^2\,(1+2x)^{2020} + ... + (2x)^{2022}

(1) ${}^{2022}C_{1011}$
(2) ${}^{2022}C_{1011} \times (2)^{1011}$
(3) ${}^{2023}C_{1011} \times (2)^{1011}$ Official answer
(4) ${}^{2023}C_{1011}$

Official answer

Option 3

NTA final key.

Chapter: Binomial Theorem
Topic: Binomial Coefficients
Idea tested: Geometric Progression of Expansions

Same idea in other shifts

Asked 3× in all

9 Apr 2024, Shift 1 · Q4The coefficient of $x^{70}$ in $x^2(1+x)^{98}+x^3(1+x)^{97}+x^4(1+x)^{96}+\ldots+x^{54}(1+x)^{46}$ is ${}^{99}C_p-{}^{46}C_q$ . Then a…HardSingle correct
25 Jun 2022, Shift 2 · Q7The coefficient of $x^{101}$ in the expression $(5+x)^{500} + x(5+x)^{499} + x^2(5+x)^{498} + ....... + x^{500}$ , $x > 0$ , isMediumSingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.