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GATE 2023 CS – Question 7

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 2 marks · Multiple choice

Consider two functions of time ($t$), $f(t) = 0.01\,t^2$ and $g(t) = 4\,t$ where $0 < t < \infty$. Now consider the following two statements: (i) For some $t > 0$, $g(t) > f(t)$. (ii) There exists a $T$, such that $f(t) > g(t)$ for all $t > T$. Which one of the following options is TRUE?

  1. only (i) is correct
  2. only (ii) is correct
  3. both (i) and (ii) are correct
  4. neither (i) nor (ii) is correct

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Correct answer: (C) both (i) and (ii) are correct

Explanation

g(t)>f(t) holds when 4t>0.01t², i.e. t<400, so (i) is true. For t>400, f(t)>g(t), so (ii) is true with T=400.