JEE Main 2021 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 17 March 2021, Shift 2, Maths Q86

Question 86 of 90 in this shift, Maths question 26 of 30, Section B.

Let 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 : 8 : 3. Then the term independent of

x

in the expansion, 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

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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
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
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.