JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 4 August 2021, Shift 2, Maths Q71

Question 71 of 90 in this shift, Maths question 11 of 30, Section A.

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

\le x

, is equal to

(1) $160\left(1-\frac{1}{e}\right)$
(2) $161$
(3) $161e$
(4) $161(e-1)$ Official answer

Official answer

Option 4

NTA final key.

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

Same idea in other shifts

Asked 3× in all

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
4 Sep 2020, Shift 2 · Q73Let $\{x\}$ and $[x]$ denote the fractional part of $x$ and the greatest integer $\leq x$ respectively of a real number $x$ . If…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.