JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 25 June 2022, Shift 1, Maths Q8

Question 8 of 90 in this shift, Maths question 8 of 30, Section A.

\frac{1}{2\cdot3^{10}}+\frac{1}{2^2\cdot3^9}+\ldots+\frac{1}{2^{10}\cdot3}=\frac{K}{2^{10}\cdot3^{10}}

, then the remainder when K is divided by 6 is :

(1) $1$
(2) $2$
(3) $3$
(4) $5$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Sequences and Series
Topic: AP and GP
Idea tested: GP Sum of n terms

Same idea in other shifts

Asked 10× in all

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3 Apr 2025, Shift 1 · Q22All five letter words are made using all the letters A, B, C, D, E and arranged as in an English dictionary with serial numbers. Let the…HardNumerical value
29 Jan 2024, Shift 1 · Q7If in a G.P. of 64 terms, the sum of all the terms is 7 times the sum of the odd terms of the G.P, then the common ratio of the G.P. is…MediumSingle correct
28 Jul 2022, Shift 2 · Q86If $\frac{6}{3^{12}}+\frac{10}{3^{11}}+\frac{20}{3^{10}}+\frac{40}{3^9}+...+\frac{10240}{3}=2^n\cdot m$ , where m is odd, then $m\cdot n$ …MediumNumerical value
25 Jun 2022, Shift 1 · Q4Let $f:\mathbf{N}\to\mathbf{R}$ be a function such that $f(x+y)=2f(x)\,f(y)$ for natural numbers $x$ and $y$ . If $f(1)=2$ , then the value…MediumSingle correct
25 Jun 2022, Shift 1 · Q30The greatest integer less than or equal to the sum of first 100 terms of the sequence…MediumNumerical value
9 Jan 2020, Shift 2 · Q57Let $a_n$ be the $n^{\mathrm{th}}$ term of a G.P. of positive terms. If $\sum_{n=1}^{100}a_{2n+1}=200$ and $\sum_{n=1}^{100}a_{2n}=100$ ,…MediumSingle correct
5 Sep 2020, Shift 1 · Q57If $2^{10}+2^{9}\cdot3^{1}+2^{8}\cdot3^{2}+....+2\cdot3^{9}+3^{10}=S-2^{11}$ , then S is equal to :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 108 of the 174 JEE Main shifts held from 2017 to 2026.