The number of points of discontinuity of the function f(x)=[ x^2 2 ]-[ x ], x ∈[0,4] , where [·] denotes the greatest integer function is ________

Correct answer: 0 Check for [(x^2)/(2)] and [ x ] becomes integers. \ 0,1, 2 , 2, 6 , 8 , 10 , 12 , 14 , 4\ Continuous at 0^ + , continuous at 4^ - [(x^2)/(2)]=[ x ] , occurs at x= 2 Not continuous

JEE Main 20257 AprilMorning Shift

Exam: JEE Main
Year: 2025
Date: 7 April
Shift: Morning Shift
Subject: Mathematics
Chapter: Continuity and Differentiability

JEE Main 2025 · 7 April · Morning Shift · Mathematics · Continuity and Differentiability

The number of points of discontinuity of the function f(x)=[ x^2 2...

The number of points of discontinuity of the function

f(\mathrm{x})=\left[\frac{\mathrm{x}^2}{2}\right]-[\sqrt{\mathrm{x}}], \mathrm{x} \in[0,4]

, where

[\cdot]

denotes the greatest integer function is ________

Correct answer

Step-by-step solution

Check for

\left[\frac{x^2}{2}\right]

and

[\sqrt{x}]

becomes integers.

\{0,1, \sqrt{2}, 2, \sqrt{6}, \sqrt{8}, \sqrt{10}, \sqrt{12}, \sqrt{14}, 4\}

Continuous at

0^{+}

, continuous at

4^{-} \left[\frac{x^2}{2}\right]=[\sqrt{x}]

, occurs at

x=\sqrt{2}

\Rightarrow

Not continuous

Practice Continuity and Differentiability on Quantrex Academy →

More from Continuity and Differentiability

Let ℝ denote the set of all real numbers. Let f : ℝ arrow ℝ be an arbitrary function and… JEE Advanced 2026 Consider the function f : (-(π)/(2), (π)/(2)) arrow (-∞, ∞) defined by f(x) = (|x| + |x… JEE Advanced 2026 For a real number α , let [α] denote the greatest integer less than or equal to α . For a… JEE Advanced 2026 For the function f(x) = e^ |x| - |x| , x ∈ ℝ , consider the following statements… JEE Main 2026 Let f(x) = cases (1)/(3), & x ≤ π/2 (b(1- x))/((π-2x)^2), & x > π/2 cases . If f is… JEE Main 2026 Let f(x) = cases x^3 + 8 ; & x Then the number of points, where the function g ∘ f is… JEE Main 2026 Let f(x)= cases e^ x-1 , & x<0 x^2-5x+6, & x ≥ 0 cases and g(x)=f(|x|)+|f(x)| . If the… JEE Main 2026 The number of points, at which the function f(x) = \ 6x, 2 + 3x^2\ + |x - 1|| |x^2… JEE Main 2026 The number of points in the interval [2, 4] , at which the function f(x) = [x^2 - x… JEE Main 2026 Let f(x)= _ θ arrow 0 ( π x-x^ ((2)/(θ)) (x-1) 1+x^ ((2)/(θ)) (x-1) ), x ∈ R . Consider… JEE Main 2026 Let [t] denote the greatest integer less than or equal to t . If the function f(x)=\… JEE Main 2026 If the function f(x)= e^ x (e^ x-x -1)+ _ e ( x+ x)-x x-x is continuous at x=0 , then the… JEE Main 2026 Let α, β ∈ ℝ be such that the function f(x)= cases 2 α(x^ 2 -2)+2 β x &, x be… JEE Main 2026 If f(x)=\ array cc a|x|+x^ 2 -2( |x|)( |x|) x &, x ≠ 0 b &, x=0 array . is continuous at… JEE Main 2026 Let f(x)= cases a x^ 2 +2 a x+3 4 x^ 2 +4 x-3 &, x ≠-(3)/(2), (1)/(2) ~b &, x=-(3)/(2)… JEE Main 2026 Let [·] denote the greatest integer function, and let f(x)= \ 2 x, x^ 2 \ . Let S = \ x… JEE Main 2026 Full Continuity and Differentiability list Continuity and Differentiability JEE Maths PYQs JEE Mathematics PYQs All JEE Main PYQs