Go To Your Study Dashboard

Get Answers to all your Questions

header-bg

Let $\mathrm{S_1, S_2, S_3 \ldots \ldots \ldots \ldots \ldots . .}$ . be squares such that for each $\mathrm{n \geq 1}$ , the length of a side of $\mathrm{S_n}$ equals the length of a diagonal of $\mathrm{S_{n+1}}$ . If the length of a side of $\mathrm{S_1\: \: is \: \: 10 \mathrm{~cm}}$ , then for which of the following values of $\mathrm{n}$ is the area of $\mathrm{S_n}$ less than $\mathrm{1 \mathrm{sq}. \mathrm{cm}}$ .?

Option: 1
5

Option: 2
6

Option: 3
7

Option: 4
8

Answers (1)

best_answer

For a square $\mathrm{A B C D}$ , the length of diagonal $\mathrm{d=a \sqrt{2}}$

As given $\mathrm{a_n=\sqrt{2} a_{n+1} ; \mathrm{n}=1,2, \ldots \ldots.}$

$\mathrm{ \therefore a_{n+1}=\frac{a_n}{\sqrt{2}}=\frac{a_{n-1}}{(\sqrt{2})^2}=\ldots \ldots \ldots . .=\frac{a_1}{(\sqrt{2})^n} }$

$\mathrm{ \Rightarrow a_n=\frac{a_1}{(\sqrt{2})^{n-1}}=\frac{10}{2^{(n-1) / 2}}}$

As area of the square $\mathrm{S_n<1,}$

$\mathrm{\Rightarrow a_n^2<1 \text { or } \frac{100}{2^{n-1}}<1 \text { or } 200<2^n}$

Or $\mathrm{2^n>200}$

As $\mathrm{ 2^7=1}$

Hence option 4 is correct.

Posted by

Kuldeep Maurya

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

50 mL of 0.2 M ammonia solution is treated with 25 mL of 0.2 M HCl. If pK_b of ammonia solution is 4.75, the pH of the mixture will be :
Option: 1 3.75
Option: 2 4.75

Trending Articles/News

anam-khan

JEE 2026: IIT admissions show major shift toward AI, data science, away from core engineering courses

anam-khan

JEE Main 2026: NIT Delhi cut-offs for BTech courses show ever-increasing demands for AI, computer skills

anam-khan

597 Eklavya school students clear JEE, NEET exams in 2024-25; Gujarat, MP lead

Latest Question