JEE Main 2024 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 6 April 2024, Shift 2, Maths Q16

Question 16 of 90 in this shift, Maths question 16 of 30, Section A.

Let

ABC

be an equilateral triangle. A new triangle is formed by joining the middle points of all sides of the triangle

ABC

and the same process is repeated infinitely many times. If

P

is the sum of perimeters and

Q

is be the sum of areas of all the triangles formed in this process, then :

(1) $P=36\sqrt{3}Q^2$
(2) $P^2=6\sqrt{3}Q$
(3) $P^2=36\sqrt{3}Q$ Official answer
(4) $P^2=72\sqrt{3}Q$

Official answer

Option 3

NTA final key.

Chapter: Sequences and Series
Topic: AP and GP
Idea tested: Infinite GP Sum

Same idea in other shifts

Asked 5× in all

4 Apr 2026, Shift 2 · Q7Let $\alpha=\frac14+\frac18+\frac1{16}+\ldots\infty$ and $\beta=\frac13+\frac19+\frac1{27}+\ldots\infty$ . Then the value of…EasySingle correct
9 Apr 2024, Shift 2 · Q7Let $a, ar, ar^2, \ldots$ be an infinite G.P. If $\sum_{n=0}^{\infty}ar^n=57$ and $\sum_{n=0}^{\infty}a^3r^{3n}=9747$ , then $a+18r$ is…MediumSingle correct
9 Jan 2020, Shift 2 · Q69If $x=\sum_{n=0}^{\infty}(-1)^n\tan^{2n}\theta$ and $y=\sum_{n=0}^{\infty}\cos^{2n}\theta$ , for $0<\theta<\frac{\pi}{4}$ , then :EasySingle correct
2 Sep 2020, Shift 1 · Q58If $|x|<1$ , $|y|<1$ and $x\neq y$ , then the sum to infinity of the following series…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 42 of the 174 JEE Main shifts held from 2017 to 2026.