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Saturday, 31 October

JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 24 June 2022, Shift 2, Maths Q5

Question 5 of 90 in this shift, Maths question 5 of 30, Section A.

Let f(x)={sin⁡(x−[x])x−[x],x∈(−2,−1)max⁡{2x,3[∣x∣]},∣x∣<11,otherwisef(x) = \begin{cases} \frac{\sin(x-[x])}{x-[x]} & , x \in (-2,-1) \\ \max\{2x, 3[|x|]\} & , |x| < 1 \\ 1 & , \text{otherwise} \end{cases} where [t][t] denotes greatest integer ≤t\leq t. If mm is the number of points where ff is not continuous and nn is the number of points where ff is not differentiable, then the ordered pair (m,n)(m, n) is:
  1. (1)(3,3)(3, 3)
  2. (2)(2,4)(2, 4)
  3. (3)(2,3)(2, 3)Official answer
  4. (4)(3,4)(3, 4)

Official answer

Option 3

NTA final key.

Chapter
Continuity and Differentiability
Topic
Continuity and Differentiability
Idea tested
Continuity involving GIF and Fractional Part

Same idea in other shifts

Asked 17× in all
  1. 2 Apr 2026, Shift 2 · Q25The number of points in the interval [2,4][2, 4], at which the function f(x)=x2−x−1⌊x⌋−12f(x) = x^2 - x - \frac{1}{\lfloor x \rfloor - \frac{1}{2}}, where…MediumNumerical value
  2. 5 Apr 2024, Shift 2 · Q10Let f:[−1,2]→Rf : [-1, 2] \to \mathbf{R} be given by f(x)=2x2+x+[x2]−[x]f(x) = 2x^2 + x + [x^2] - [x], where [t][t] denotes the greatest integer less than or equal…MediumSingle correct
  3. 6 Apr 2024, Shift 2 · Q24Let [t][t] denote the greatest integer less than or equal to tt. Let f:[0,∞)→Rf:[0,\infty)\to\mathbb{R} be a function defined by…MediumNumerical value
  4. 27 Jan 2024, Shift 1 · Q8Consider the function.…HardSingle correct
  5. 6 Apr 2023, Shift 1 · Q25Let a∈Za\in\mathbb{Z} and [t][t] be the greatest integer ≤t\le t. Then the number of points, where the function f(x)=[a+13sin⁡x]f(x)=[a+13\sin x],…HardNumerical value
  6. 11 Apr 2023, Shift 1 · Q7Let f(x)=[x2−x]+∣−x+[x]∣f(x) = [x^2 - x] + |-x + [x]|, where x∈Rx \in \mathbb{R} and [t][t] denotes the greatest integer less than or equal to tt. Then, ff isMediumSingle correct
  7. 12 Apr 2023, Shift 1 · Q25Let [x][x] be the greatest integer ≤x\le x. Then the number of points in the interval (−2,1)(-2,1), where the function…MediumNumerical value
  8. 29 Jul 2022, Shift 2 · Q26If [t][t] denotes the greatest integer ≤t\leq t, then the number of points, at which the function…HardNumerical 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.