JEE Main 2024 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 9 April 2024, Shift 2, Maths Q7

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

Let

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 equal to

(1) $27$
(2) $31$ Official answer
(3) $38$
(4) $46$

Official answer

Option 2

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
6 Apr 2024, Shift 2 · Q16Let $ABC$ be an equilateral triangle. A new triangle is formed by joining the middle points of all sides of the triangle $ABC$ and the…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.