JEE Main 2021 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 16 March 2021, Shift 2, Maths Q74

Question 74 of 90 in this shift, Maths question 14 of 30, Section A.

Consider the integral

I=\int_0^{10}\frac{[x]\,e^{[x]}}{e^{x-1}}\,dx

, where

[x]

denotes the greatest integer less than or equal to

x

. Then the value of I is equal to :

(1) $45\,(e+1)$
(2) $9\,(e+1)$
(3) $45\,(e-1)$ Official answer
(4) $9\,(e-1)$

Official answer

Option 3

NTA final key.

Chapter: Integrals
Topic: Definite Integral Properties
Idea tested: Greatest Integer Function Integrals

Same idea in other shifts

Asked 9× in all

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6 Apr 2024, Shift 2 · Q25Let $[t]$ denote the largest integer less than or equal to $t$ . If…HardNumerical value
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29 Jun 2022, Shift 1 · Q17 $\int_0^5 \cos\left(\pi\left(x - \left[\frac{x}{2}\right]\right)\right)dx$ , where $[t]$ denotes greatest integer less than or equal to…MediumSingle correct
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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 42 of the 174 JEE Main shifts held from 2017 to 2026.