JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 22 July 2021, Shift 2, Maths Q79

Question 79 of 90 in this shift, Maths question 19 of 30, Section A.

Let

[x]

denote the greatest integer less than or equal to

x

. Then, the values of

x\in\mathbf{R}

satisfying the equation

[e^x]^2+[e^x+1]-3=0

lie in the interval :

(1) $[0, 1/e)$
(2) $[1, e)$
(3) $[0, \log_e2)$ Official answer
(4) $[\log_e2, \log_e3)$

Official answer

Option 3

NTA final key.

Chapter: Relations and Functions
Topic: Functions and Domain
Idea tested: Domain Constraints of Greatest Integer Function

Same idea in other shifts

Asked 3× in all

6 Apr 2023, Shift 2 · Q1[English stem not rendered in the PDF; reconstructed from the Hindi copy] Let the function $f(x)=\frac{1}{\sqrt{\lceil x\rceil-x}}$ , where…MediumTwo statements
11 Apr 2023, Shift 2 · Q2The domain of the function $f(x) = \frac{1}{\sqrt{[x]^2 - 3[x] - 10}}$ is (where $[x]$ denotes the greatest integer less than or equal to…MediumSingle 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.