JEE Main 2021 · MathsNumerical answerNumerical valueMediumApplication

JEE Main 25 February 2021, Shift 1, Maths Q85

Question 85 of 90 in this shift, Maths question 25 of 30, Section B.

Let

\mathrm{A}_1, \mathrm{A}_2, \mathrm{A}_3, .....

be squares such that for each

\mathrm{n} \geq 1

, the length of the side of

\mathrm{A}_\mathrm{n}

equals the length of diagonal of

\mathrm{A}_{\mathrm{n}+1}

. If the length of

\mathrm{A}_1

is 12 cm, then the smallest value of n for which area of

\mathrm{A}_\mathrm{n}

is less than one, is __________.

Official answer

NTA final key.

Chapter: Sequences and Series
Topic: AP and GP
Idea tested: GP General Term

Same idea in other shifts

Asked 15× in all

3 Apr 2025, Shift 1 · Q6Let $a_1, a_2, a_3, \ldots$ be a G.P. of increasing positive numbers. If $a_3 a_5 = 729$ and $a_2 + a_4 = \frac{111}{4}$ , then…EasySingle correct
7 Apr 2025, Shift 2 · Q7If the sum of the second, fourth and sixth terms of a G.P. of positive terms is 21 and the sum of its eighth, tenth and twelfth terms is…MediumSingle correct
4 Apr 2024, Shift 1 · Q9Let the first three terms $2$ , $p$ and $q$ , with $q \neq 2$ , of a G.P. be respectively the $7^{th}$ , $8^{th}$ and $13^{th}$ terms of an…MediumSingle correct
8 Apr 2024, Shift 2 · Q8In an increasing geometric progression of positive terms, the sum of the second and sixth terms is $\frac{70}{3}$ and the product of the…MediumSingle correct
30 Jan 2024, Shift 2 · Q6Let $a$ and $b$ be be two distinct positive real numbers. Let $11^{\mathrm{th}}$ term of a GP, whose first term is $a$ and third term is…EasySingle correct
31 Jan 2024, Shift 2 · Q7Let $2^{nd}$ , $8^{th}$ and $44^{th}$ terms of a non-constant A. P. be respectively the $1^{st}$ , $2^{nd}$ and $3^{rd}$ terms of a G. P. If…MediumSingle correct
13 Apr 2023, Shift 2 · Q8Let $a_1, a_2, a_3, \ldots$ be a G.P. of increasing positive numbers. Let the sum of its $6^{th}$ and $8^{th}$ terms be $2$ and the…MediumSingle correct
26 Jun 2022, Shift 2 · Q27If $a_1\ (> 0), a_2, a_3, a_4, a_5$ are in a G.P., $a_2 + a_4 = 2a_3 + 1$ and $3a_2 + a_3 = 2a_4$ , then $a_2 + a_4 + 2a_5$ is equal to…MediumNumerical 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.