JEE Main 2021 · MathsNumerical answerNumerical valueMediumCalculation

JEE Main 25 July 2021, Shift 2, Maths Q87

Question 87 of 90 in this shift, Maths question 27 of 30, Section B.

If the co-efficients of

x^7

and

x^8

in the expansion of

\left(2+\frac{x}{3}\right)^n

are equal, then the value of n is equal to __________.

Official answer

NTA final key.

Chapter: Binomial Theorem
Topic: Binomial Coefficients
Idea tested: Ratio of Consecutive Coefficients

Same idea in other shifts

Asked 9× in all

4 Apr 2024, Shift 2 · Q4If the coefficients of $x^4$ , $x^5$ and $x^6$ in the expansion of $(1+x)^n$ are in the arithmetic progression, then the maximum value of…MediumSingle correct
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8 Apr 2023, Shift 1 · Q8If the coefficients of three consecutive terms in the expansion of $(1+x)^n$ are in the ratio $1:5:20$ , then the coefficient of the fourth…MediumSingle correct
11 Apr 2023, Shift 2 · Q8The sum of the coefficients of three consecutive terms in the binomial expansion of $(1 + x)^{n+2}$ , which are in the ratio $1:3:5$ , is…MediumSingle correct
27 Jul 2022, Shift 2 · Q23Let for the $9^{th}$ term in the binomial expansion of $(3 + 6x)^n$ , in the increasing powers of $6x$ , to be the greatest for…HardNumerical value
17 Mar 2021, Shift 2 · Q86Let the coefficients of third, fourth and fifth terms in the expansion of $\left(x+\frac{a}{x^2}\right)^n$ , $x\neq 0$ , be in the ratio 12…MediumNumerical value
2 Sep 2020, Shift 2 · Q71For a positive integer n, $\left(1+\frac{1}{x}\right)^n$ is expanded in increasing powers of $x$ . If three consecutive coefficients in…MediumNumerical value
4 Sep 2020, Shift 2 · Q56If for some positive integer n, the coefficients of three consecutive terms in the binomial expansion of $(1+x)^{n+5}$ are in the ratio…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.