Learn

Friday, 9 October

JEE Main 2024 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 8 April 2024, Shift 1, Maths Q24

Question 24 of 90 in this shift, Maths question 24 of 30, Section B.

Let α=∑r=0n(4r2+2r+1) nCr\alpha=\sum_{r=0}^{n}(4r^2+2r+1)\,{}^nC_r and β=(∑r=0nnCrr+1)+1n+1\beta=\left(\sum_{r=0}^{n}\frac{{}^nC_r}{r+1}\right)+\frac{1}{n+1}. If 140<2αβ<281140<\frac{2\alpha}{\beta}<281, then the value of nn is ____________.

Official answer

5

NTA final key.

Chapter
Binomial Theorem
Topic
Binomial Coefficients
Idea tested
Second Derivative Method for Sums

Same idea in other shifts

Asked 2× in all
  1. 4 Apr 2025, Shift 2 · Q7If 12⋅(15C1)+22⋅(15C2)+32⋅(15C3)+…+152⋅(15C15)=2m⋅3n⋅5k1^2\cdot({}^{15}C_1)+2^2\cdot({}^{15}C_2)+3^2\cdot({}^{15}C_3)+\ldots+15^2\cdot({}^{15}C_{15})=2^m\cdot3^n\cdot5^k, where…MediumSingle 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 42 of the 174 JEE Main shifts held from 2017 to 2026.