PYQ Vault
EbooksTutor

Points of discontinuity of a function with the greatest integer of a polynomial

This type of question, asked 7 times: 14 Jun 2022, 12 Apr 2023, 5 Apr 2024, 6 Apr 2024, 7 Apr 2025, 22 Jan 2026 S2, 2 Apr 2026 S2. All 7 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    14 Jun 2022

    85
    The number of points where the function
    f(x)={∣2x2−3x−7∣ if x≤−1[4x2−1] if −1<x<1∣x+1∣+∣x−2∣ if x≥1f(x) =\left\{ \begin{matrix} \left| 2x^{2}- 3x- 7 \right| & \text{~if~} & x\leq - 1 \\ \left\lbrack 4x^{2}- 1 \right\rbrack & \text{~if~} & - 1 <x< 1 \\ |x+ 1| + |x- 2| & \text{~if~} & x\geq 1 \end{matrix} \right.
    [t] denotes the greatest integer ≤t\leq t, is discontinuous is

  2. Question 2

    12 Apr 2023

    83
    Let [x]\lbrack x\rbrack be the greatest integer ≤x\leq x. Then the number of points in the interval (−2,1)( - 2,1), where the function f(x)=∣[x]∣+x−[x]f(x) = |\lbrack x\rbrack| +\sqrt{x - \lbrack x\rbrack} is discontinuous is

  3. Question 3

    5 Apr 2024

    151
    Let f:[−1,2]→Rf:\lbrack - 1,2\rbrack \rightarrow R be given by f(x)=2x2+x+[x2]−[x]f(x) = 2x^{2}+ x +\left\lbrack x^{2} \right\rbrack- \lbrack x\rbrack, where [t]\lbrack t\rbrack denotes the greatest integer less than or equal to t. The number of points, where ff is not continuous, is:

    Tap an option to check your answer.

  4. Question 4

    6 Apr 2024

    171
    Let [t]\lbrack t\rbrack denote the greatest integer less than or equal to tt. Let f:[0,∞)→Rf:\lbrack 0,\infty) \rightarrow R be a function defined by f(x)=[x2+3]−[x]f(x) =\left\lbrack \frac{x}{2}+ 3 \right\rbrack- \lbrack\sqrt{x}\rbrack. Let SS be the set of all points in the interval [0,8]\lbrack 0,8\rbrack at which ff is not continuous. Then ∑a∈Sa\sum_{a \in S} a is equal to

  5. Question 5

    7 Apr 2025

    71
    The number of points of discontinuity of the function f(x)=[x22]−[x],x∈[0,4]f(x) = \left\lbrack \frac{x^{2}}{2} \right\rbrack - \lbrack\sqrt{x}\rbrack,x \in \lbrack 0,4\rbrack, where denotes the greatest integer function is

  6. Question 6

    22 Jan 2026 S2

    65
    Let [∙]\lbrack \bullet \rbrack denote the greatest integer function, and let f(x)=min{2x,x2}f(x) = min\left\{ \sqrt{2}x,x^{2} \right\}. Let S={x∈(−2,2):\mathbf{S = \{ x \in ( - 2,2):} the function g(x)=∣x∣[x2]g(x) = |x|\left\lbrack x^{2} \right\rbrack is discontinuous at x}\}. Then ∑x∈Sf(x)\sum_{x \in S} f(x) equals :

    Tap an option to check your answer.

  7. Question 7

    2 Apr 2026 S2

    75
    The number of points in the interval [2,4], at which the function f(x)=[x2−x−12]f(x) = \left\lbrack x^{2} - x - \frac{1}{2} \right\rbrack, where [⋅]\lbrack \cdot \rbrack denotes the greatest integer function, is discontinuous, is ____\_\_\_\_ .