in Quantitative Aptitude edited by
1 vote
1 vote

Consider two functions of time $(t),$
f(t)=0.01 t^2 \\
g(t)=4 t
where $0<t<\infty.$

Now consider the following two statements:

  1. For some $t>0, g(t)>f(t)$.
  2. There exists a $T,$ such that $f(t)>g(t)$ for all $t>T$.

Which one of the following options is $\text{TRUE}?$

  1. only (i) is correct
  2. only (ii) is correct
  3. both (i) and (ii) are correct
  4. neither (i) nor (ii) is correct
in Quantitative Aptitude edited by

3 Answers

3 votes
3 votes




and $0< t< \infty$

for option $(i)$,

take $t=1$,Now,



So, here exists some $t$ ,t=1 , for which $g(t)>f(t).$ So $(i)$ is true .

for option $(ii)$,There exists some $ T=1000$(say) .Now any $t>T$ , $f(t)>g(t)$ .

So option (II) is also true .

This question is nothing but Big oh definition .

 $g(t)\leq cf(t)$ for all $t>T$ and $c>0$ .

So correct option is (C) .

2 votes
2 votes
For (i) :

f(1) = 0.01   and   g(1) = 4

So, there exists a t = 1, such that (i) is true.

(ii) matches the definition of small oh notation

Here, g(t) = o(f(t)) is true.

So, f(t) > g(t)  is always true for all t > T

Hence, (ii) is also correct. Option D is the correct answer.

1 comment

Edit the answer, Option C is correct.
0 votes
0 votes
C option is correct

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