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Saturday, 31 October

JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 28 June 2022, Shift 1, Maths Q8

Question 8 of 90 in this shift, Maths question 8 of 30, Section A.

Let f:R→Rf:\mathbb{R}\to\mathbb{R} be defined as f(x)={[ex],x<0aex+[x−1],0≤x<1b+[sin⁡(πx)],1≤x<2[e−x]−c,x≥2f(x)=\begin{cases}[e^x], & x<0\\ ae^x+[x-1], & 0\le x<1\\ b+[\sin(\pi x)], & 1\le x<2\\ [e^{-x}]-c, & x\ge2\end{cases} where a,b,c∈Ra, b, c\in\mathbb{R} and [t][t] denotes greatest integer less than or equal to tt. Then, which of the following statements is true ?
  1. (1)There exists a,b,c∈Ra, b, c\in\mathbb{R} such that ff is continuous on R\mathbb{R}.
  2. (2)If ff is discontinuous at exactly one point, then a+b+c=1a+b+c=1
  3. (3)If ff is discontinuous at exactly one point, then a+b+c≠1a+b+c\neq1Official answer
  4. (4)ff is discontinuous at atleast two points, for any values of a,ba, b and cc

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.