JEE Main 2021 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 26 August 2021, Shift 2, Maths Q74

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

If the value of the integral

\int_0^5\frac{x+[x]}{\mathrm{e}^{x-[x]}}\,\mathrm{d}x=\alpha\mathrm{e}^{-1}+\beta

, where

\alpha,\beta\in\mathbf{R}

5\alpha+6\beta=0

, and

[x]

denotes the greatest integer less than or equal to

x

; then the value of

(\alpha+\beta)^2

is equal to :

(1) $25$ Official answer
(2) $36$
(3) $100$
(4) $16$

Official answer

Option 1

NTA final key.

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

Same idea in other shifts

Asked 29× in all

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2 Apr 2025, Shift 1 · Q23Let $[\cdot]$ denote the greatest integer function. If $\int_0^{e^3}\left[\frac{1}{e^{x-1}}\right]dx=\alpha-\log_e2$ , then $\alpha^3$ is…MediumNumerical value
3 Apr 2025, Shift 1 · Q19Let the domain of the function $f(x) = \log_2 \log_4 \log_6 (3 + 4x - x^2)$ be $(a, b)$ . If…HardSingle correct
6 Apr 2024, Shift 2 · Q25Let $[t]$ denote the largest integer less than or equal to $t$ . If…HardNumerical value
30 Jan 2024, Shift 1 · Q25The value of $9\int_0^9\left[\sqrt{\frac{10x}{x+1}}\right]dx$ , where $[t]$ denotes the greatest integer less than or equal to $t$ , is…HardNumerical value
8 Apr 2023, Shift 1 · Q24Let $[t]$ denote the greatest integer $\le t$ . Then $\frac{2}{\pi}\int_{\pi/6}^{5\pi/6}(8[\operatorname{cosec}x]-5[\cot x])\,dx$ is equal…HardNumerical value
8 Apr 2023, Shift 2 · Q26Let $[t]$ denote the greatest integer function. If $\int_0^{2.4}[x^2]\,dx = \alpha + \beta\sqrt{2} + \gamma\sqrt{3} + \delta\sqrt{5}$ ,…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.