JEE Main 2021 · MathsNumerical answerNumerical valueMediumCalculation

JEE Main 25 July 2021, Shift 2, Maths Q83

Question 83 of 90 in this shift, Maths question 23 of 30, Section B.

Let

n\,\epsilon\,\mathbf{N}

and

[x]

denote the greatest integer less than or equal to

x

. If the sum of

(n+1)

terms

{}^nC_0,\ 3\cdot{}^nC_1,\ 5\cdot{}^nC_2,\ 7\cdot{}^nC_3,\ .....

is equal to

2^{100}\cdot101

, then

2\left[\frac{n-1}{2}\right]

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
18 Mar 2021, Shift 2 · Q89Let ${}^nC_r$ denote the binomial coefficient of $x^r$ in the expansion of $(1+x)^n$ . If…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.