JEE Main 2021 · MathsMultiple choiceSingle correctEasyApplication

JEE Main 26 February 2021, Shift 1, Maths Q80

Question 80 of 90 in this shift, Maths question 20 of 30, Section A.

The value of

\sum_{n=1}^{100}\int_{n-1}^{n} e^{x-[x]}\,dx

, where

[x]

is the greatest integer

\le x

, is :

(1) $100(1-e)$
(2) $100(1+e)$
(3) $100e$
(4) $100(e-1)$ 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

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
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.