JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 26 August 2021, Shift 1, Maths Q67

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

If the sum of an infinite GP

a, ar, ar^2, ar^3, \ldots

is 15 and the sum of the squares of its each term is 150, then the sum of

ar^2, ar^4, ar^6, \ldots

is :

(1) $\frac{5}{2}$
(2) $\frac{1}{2}$ Official answer
(3) $\frac{9}{2}$
(4) $\frac{25}{2}$

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 15× 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 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
15 Apr 2023, Shift 1 · Q24If the sum of the series…HardNumerical value
27 Jul 2022, Shift 2 · Q7Let the sum of an infinite G.P., whose first term is a and the common ratio is r, be 5. Let the sum of its first five terms be…MediumSingle correct
26 Jun 2022, Shift 2 · Q3If $A = \sum_{n=1}^{\infty} \frac{1}{(3 + (-1)^n)^n}$ and $B = \sum_{n=1}^{\infty} \frac{(-1)^n}{(3 + (-1)^n)^n}$ , then $\frac{A}{B}$ is…MediumSingle correct
27 Jun 2022, Shift 1 · Q3If $x=\sum_{n=0}^{\infty} a^n$ , $y=\sum_{n=0}^{\infty} b^n$ , $z=\sum_{n=0}^{\infty} c^n$ , where a, b, c are in A.P. and $|a|<1$ , $|b|<1$ ,…MediumSingle correct
28 Jun 2022, Shift 2 · Q25Let for $n=1, 2, \ldots, 50$ , $S_n$ be the sum of the infinite geometric progression whose first term is $n^2$ and whose common ratio is…HardNumerical 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.