JEE Main 2022 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 27 July 2022, Shift 2, Maths Q23

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

Let for the

9^{th}

term in the binomial expansion of

(3 + 6x)^n

, in the increasing powers of

6x

, to be the greatest for

x = \frac{3}{2}

, the least value of n is

n_0

. If k is the ratio of the coefficient of

x^6

to the coefficient of

x^3

, then

k + n_0

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
6 Apr 2024, Shift 1 · Q23If the second, third and fourth terms in the expansion of $(x+y)^n$ are $135$ , $30$ and $\frac{10}{3}$ , respectively, then $6(n^3+x^2+y)$ …MediumNumerical value
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
25 Jul 2021, Shift 2 · Q87If 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…MediumNumerical 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.