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Friday, 9 October

JEE Main 2021 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 16 March 2021, Shift 2, Maths Q69

Question 69 of 90 in this shift, Maths question 9 of 30, Section A.

Let α∈R\alpha\in\mathbf R be such that the function f(x)={cos⁡−1(1−{x}2)sin⁡−1(1−{x}){x}−{x}3,x≠0α,x=0f(x)=\begin{cases}\frac{\cos^{-1}(1-\{x\}^2)\sin^{-1}(1-\{x\})}{\{x\}-\{x\}^3}, & x\neq0\\ \alpha, & x=0\end{cases} is continuous at x=0x=0, where {x}=x−[x]\{x\}=x-[x], [x][x] is the greatest integer less than or equal to xx. Then :
  1. (1)α=0\alpha=0
  2. (2)no such α\alpha existsOfficial answer
  3. (3)α=π2\alpha=\frac{\pi}{\sqrt2}
  4. (4)α=π4\alpha=\frac{\pi}{4}

Official answer

Option 2

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 7× 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. 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
  3. 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
  4. 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
  5. 24 Jun 2022, Shift 1 · Q25The number of points where the function…HardNumerical value
  6. 9 Jan 2020, Shift 2 · Q58Let [t][t] denote the greatest integer ≤t\le t and lim⁡x→0x[4x]=A\lim_{x\to0}x\left[\frac{4}{x}\right]=A. Then the function, f(x)=[x2]sin⁡(πx)f(x)=[x^2]\sin(\pi x) is…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 42 of the 174 JEE Main shifts held from 2017 to 2026.