time complexity

Question

I got this question from here https://gateoverflow.in/169286/time-complexity

Is this Question Correct i have doubt . If correct please explain

Which of the following statements is/are TRUE? 
$i)$ The time complexity of recurrence relation $A(n) = 3A(n/2)+n^{2} $is asymptotically faster than $T(n) = 4T(n/2)+ n^{2}$ 

$ii)$ The time complexity of recurrence relation $A(n) = 512 A(n/2) + O(n^{50})$ is asymptotically faster than $T(n) = 7T(n-53) + O(1)$, $T(0) = 1$.

i am getting till here

$I)O(n^{2}) < O( n^{2}log n)$  so $O( n^{2} log n)$ is asymptotically faster

$II)O( 7 ^ {n/53}) > O(n ^{50})$ so $O( 7 ^ {n/53})$ is asymptotically faster

But i am not able to get the answer because of question statement .

 

Comments

@srestha

mam, what is the relation btw this question and the link ( you provided ).

i didn't get any relation between them

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@Shaik

ok,sorry,I might misinterpreted

Actually what I mean $O(n-x)$ might have time complexity $O(nlog n)$ which must be lesser than $O(n^{50})$ 

Here is another interpretation what asymtotically faster means https://courses.csail.mit.edu/6.006/fall11/psets/ps1_solutions.pdf

So, 2nd one might correct

but how 1st one can be correct? It cannot be

right?

 

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2nd also not correct

due to O( n⁵⁰ )  is O( 7^n/53 )