JEE Main 2024 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 30 January 2024, Shift 2, Maths Q24

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

Let

\alpha = \sum_{k=0}^{n} \left(\frac{({}^nC_k)^2}{k+1}\right)

and

\beta = \sum_{k=0}^{n-1} \left(\frac{{}^nC_k\, {}^nC_{k+1}}{k+2}\right)

. If

5\alpha = 6\beta

, then

n

equals ________.

Official answer

NTA final key.

Chapter: Binomial Theorem
Topic: Binomial Coefficients
Idea tested: Definite Integral Method for Beta-like Sums

Same topic in other shifts

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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.