JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 25 June 2022, Shift 2, Maths Q7

Question 7 of 90 in this shift, Maths question 7 of 30, Section A.

The coefficient of

x^{101}

in the expression

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

x > 0

, is

(1) ${}^{501}C_{101}\,(5)^{399}$ Official answer
(2) ${}^{501}C_{101}\,(5)^{400}$
(3) ${}^{501}C_{100}\,(5)^{400}$
(4) ${}^{500}C_{101}\,(5)^{399}$

Official answer

Option 1

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
30 Jul 2022, Shift 2 · Q66The coefficient of $x^{1011}$ in the expression $(1+2x)^{2022} + 2x\,(1+2x)^{2021} + (2x)^2\,(1+2x)^{2020} + ... + (2x)^{2022}$ 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.