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

\alpha=\sum_{r=0}^{n}(4r^2+2r+1)\,{}^nC_r

and

\beta=\left(\sum_{r=0}^{n}\frac{{}^nC_r}{r+1}\right)+\frac{1}{n+1}

. If

140<\frac{2\alpha}{\beta}<281

, then the value of

n

is ____________.

Official answer

NTA final key.

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

Same idea in other shifts

Asked 3× in all

4 Apr 2025, Shift 2 · Q7If $1^2\cdot({}^{15}C_1)+2^2\cdot({}^{15}C_2)+3^2\cdot({}^{15}C_3)+\ldots+15^2\cdot({}^{15}C_{15})=2^m\cdot3^n\cdot5^k$ , where…MediumSingle correct
26 Aug 2021, Shift 1 · Q66If $^{20}C_r$ is the co-efficient of $x^r$ in the expansion of $(1+x)^{20}$ , then the value of $\sum_{r=0}^{20} r^2\,{}^{20}C_r$ is equal…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 108 of the 174 JEE Main shifts held from 2017 to 2026.