JEE Main 2026 · MathsMultiple choiceSingle correctEasyCalculation

JEE Main 4 April 2026, Shift 2, Maths Q7

Question 7 of 75 in this shift, Maths question 7 of 25, Section A.

Let

\alpha=\frac14+\frac18+\frac1{16}+\ldots\infty

and

\beta=\frac13+\frac19+\frac1{27}+\ldots\infty

. Then the value of

(0.2)^{\log_{\sqrt5}(\alpha)}+(0.04)^{\log_5(\beta)}

is equal to:

(1)4
(2)5
(3)8Official answer
(4)25

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

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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.