JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 3 August 2021, Shift 2, Maths Q67

Question 67 of 90 in this shift, Maths question 7 of 30, Section A.

If '

m

' is the arithmetic mean of two distinct real numbers

l

and

n

(l, n > 1)

and

G_1

G_2

and

G_3

are three geometric means between

l

and

n

, then

G_1^4 + 2G_2^4 + G_3^4

equals

(1) $2l^2mn$
(2) $4lm^2n$ Official answer
(3) $4lmn^2$
(4) $2lm^2n^2$

Official answer

Option 2

NTA final key.

Chapter: Sequences and Series
Topic: AP and GP
Idea tested: Arithmetic and Geometric Means

Same idea in other shifts

Asked 4× in all

15 Apr 2023, Shift 1 · Q8Let $A_1$ and $A_2$ be two arithmetic means and $G_1, G_2, G_3$ be three geometric means of two distinct positive numbers. Then…MediumSingle correct
28 Jun 2022, Shift 2 · Q5If n arithmetic means are inserted between a and 100 such that the ratio of the first mean to the last mean is $1:7$ and $a+n=33$ , then…MediumSingle correct
3 Sep 2020, Shift 2 · Q73If m arithmetic means (A.Ms) and three geometric means (G.Ms) are inserted between 3 and 243 such that $4^{th}$ A.M. is equal to $2^{nd}$ …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.