JEE Main 2024 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 6 April 2024, Shift 1, Maths Q23

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

If 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)

is equal to __________

Official answer

806

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
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
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.