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Saturday, 31 October

JEE Main 2023 · MathsMultiple choiceTwo statementsMediumConceptual

JEE Main 6 April 2023, Shift 2, Maths Q1

Question 1 of 90 in this shift, Maths question 1 of 30, Section A.

[English stem not rendered in the PDF; reconstructed from the Hindi copy] Let the function f(x)=1⌈x⌉−xf(x)=\frac{1}{\sqrt{\lceil x\rceil-x}}, where ⌈x⌉\lceil x\rceil is the smallest integer ≥x\geq x, have domain AA and range BB. Then the statements (S1) : A∩B=(1,∞)−NA\cap B=(1,\infty)-\mathbb{N} and (S2) : A∪B=(1,∞)A\cup B=(1,\infty)
  1. (1)only (S1) is trueOfficial answer
  2. (2)only (S2) is true
  3. (3)both (S1) and (S2) are true
  4. (4)neither (S1) nor (S2) is true

Official answer

Option 1

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
  1. 11 Apr 2023, Shift 2 · Q2The domain of the function f(x)=1[x]2−3[x]−10f(x) = \frac{1}{\sqrt{[x]^2 - 3[x] - 10}} is (where [x][x] denotes the greatest integer less than or equal to…MediumSingle correct
  2. 22 Jul 2021, Shift 2 · Q79Let [x][x] denote the greatest integer less than or equal to xx. Then, the values of x∈Rx\in\mathbf{R} satisfying the equation…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.