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JEE Main 20246 AprilEvening Shift
Exam
JEE Main
Year
2024
Date
6 April
Shift
Evening Shift
Subject
Mathematics
Chapter
Continuity and Differentiability

JEE Main 2024 · 6 April · Evening Shift · Mathematics · Continuity and Differentiability

Let [t] denote the greatest integer less than or equal to t . Let...

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

Correct answer

0

Step-by-step solution

[x2+3]\left[\frac{x}{2}+3\right] is discontinuous at x=2,4,6,8xx=2,4,6,8 \sqrt{\mathrm{x}} is discontinuous at x=1,4F(x)\mathrm{x}=1,4 \mathrm{F}(\mathrm{x}) is discontinuous at x=1,2,6,8∑a=1+2+6+8=17\mathrm{x}=1,2,6,8 \sum \mathrm{a}=1+2+6+8=17
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