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Friday, 9 October

JEE Main 2021 · MathsMultiple choiceSingle correctMediumConceptual

JEE Main 25 July 2021, Shift 1, Maths Q64

Question 64 of 90 in this shift, Maths question 4 of 30, Section A.

Let f:[0,∞)→[0,∞)f:[0,\infty)\to[0,\infty) be defined as f(x)=∫0x[y] dyf(x)=\int_0^x[y]\,dy where [x][x] is the greatest integer less than or equal to xx. Which of the following is true ?
  1. (1)ff is differentiable at every point in [0,∞)[0,\infty).
  2. (2)ff is continuous at every point in [0,∞)[0,\infty) and differentiable except at the integer points.Official answer
  3. (3)ff is continuous everywhere except at the integer points in [0,∞)[0,\infty).
  4. (4)ff is both continuous and differentiable except at the integer points in [0,∞)[0,\infty).

Official answer

Option 2

NTA final key.

Chapter
Continuity and Differentiability
Topic
Continuity and Differentiability
Idea tested
Continuity and Differentiability of Integral Functions

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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.