JEE Main 2021 · MathsNumerical answerNumerical valueMediumCalculation

JEE Main 18 March 2021, Shift 2, Maths Q89

Question 89 of 90 in this shift, Maths question 29 of 30, Section B.

Let

{}^nC_r

denote the binomial coefficient of

x^r

in the expansion of

(1+x)^n

. If

\sum_{k=0}^{10}(2^2+3k)\,{}^nC_k=\alpha\cdot3^{10}+\beta\cdot2^{10}

\alpha, \beta\in\mathbb{R}

, then

\alpha+\beta

is equal to ___________.

Official answer

NTA final key.

Chapter: Binomial Theorem
Topic: Binomial Coefficients
Idea tested: Binomial Coefficients with AP Multiplier

Same idea in other shifts

Asked 3× in all

3 Apr 2025, Shift 1 · Q8If $\sum_{r=1}^{9}\left(\frac{r+3}{2^r}\right)\cdot {}^9C_r = \alpha\left(\frac{3}{2}\right)^9 - \beta$ , $\alpha, \beta \in \mathbb{N}$ ,…MediumSingle correct
25 Jul 2021, Shift 2 · Q83Let $n\,\epsilon\,\mathbf{N}$ and $[x]$ denote the greatest integer less than or equal to $x$ . If the sum of $(n+1)$ terms…MediumNumerical value

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.