Test by Bikram | Mock GATE | Test 1 | Question: 32

Question

Let $f\left ( n \right )$m  $g\left ( n \right )$ and $h\left ( n \right )$ be functions whose domain is a subset of positive integers such that $f\left ( n \right )= O\left (n^{2}\right), g\left ( n \right )= O\left(n^{3}\right), h\left ( n \right )= O\left(n^{4}\right).$ Then:

1. $f \left ( n \right ) +g \left ( n \right )= O \left(n^{3}\right)$   
2. $h \left ( n \right ) -g \left ( n \right )=O \left ( n \right )$    
3. $f \left ( n \right ).g \left ( n \right )=O\left( n^{4}\right)$   
4. $h \left ( n \right ) .g \left ( n \right ) =O\left(n^{7}\right)$

Which of the above is/are incorrect?

• A. $(d)$ $only$
• B. $(c)$ $only$
• C. $(b)$ $and$ $(d)$ $only$
• D. $(b)$ $and$ $(c)$ $only$

Answer 1

Here  (a) is correct because f(n) = O(n^2) and g(n) = O(n^3), and f(n) + g(n) = O(n^3) (Addition Rule asymptotic behavior)
Similarly item (d) is also correct according to the Multiplication Rule for asymptotic behavior. Hence the answer is (D).

Comments

@Bikram sir i have given answer but it is showing answer d can you please check once

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yes for this questin answer D is correct option.

what option you put as an answer ? is it D , if yes plz post that snap.

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No Sir I have given option A , after reading 1st line , I think the answer is option A sry

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@bikram sir  

a-true

b-true

d-true

then option C is the correct ans

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if f(n) = O(n²),    g(n) = O(n³), then how     option  c)  f(n).g(n)=O(n⁴) is possible ?

also if   h(n) = O(n⁴)    and g(n) = O(n³) then how   option  b)   h(n)-g(n)=O(n) is possible ?

so option b) and c) is incorrect hence D) is correct/ valid option.

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Sir (a) and (d) are right. but there is no option having (a)

and you are saying option D is correct which is containing (b) and (d) but (b) is not correct. so how option D is the answer?

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oh no...question was asking which is incorrect.. sorry...i have to be more careful

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@vineet

why not read question carefully !!

it says Which of the above is/are incorrect ? 

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can someone explain option b why it is wrong.