JEE Main 2020 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 4 September 2020, Shift 2, Maths Q73

Question 73 of 75 in this shift, Maths question 23 of 25.

Let

\{x\}

and

[x]

denote the fractional part of

x

and the greatest integer

\leq x

respectively of a real number

x

. If

\int_0^n \{x\}\,dx

\int_0^n [x]\,dx

and

10(n^2-n)

(n \in \mathbf{N}, n > 1)

are three consecutive terms of a G.P., then n is equal to ________.

Official answer

21.00

NTA final key (Sep 2020).

Chapter: Integrals
Topic: Definite Integral Properties
Idea tested: Fractional Part Function Integrals

Same idea in other shifts

Asked 3× in all

4 Aug 2021, Shift 2 · Q71If $u+v+w=91$ , and $2u=3v=4w$ , then the value of $\int_{u-v+w}^{2u+v+4w}e^{(x-[x])}\,dx$ , where $[x]$ denotes the greatest integer…MediumSingle correct
26 Feb 2021, Shift 1 · Q80The value of $\sum_{n=1}^{100}\int_{n-1}^{n} e^{x-[x]}\,dx$ , where $[x]$ is the greatest integer $\le x$ , is :EasySingle 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.